Quiz Results

Quiz	Differentiation
Name	O l i v e r S t a l l a r d
Email	S t a l l a r d O N @ d u l w i c h . o r g . u k
Result	PASSED
Score	20 / 22 (90.9%)
Passing score	17.6
Quiz took	15 min 15 sec
Quiz finished at	2025-02-02 17:19:25

Differentiate with respect to x\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}} y = {6x}^{2}

Awarded Points: 1

Correct Response: \frac{dy}{dx}=12x

User Response: \frac{dy}{dx}=12x

Differentiate with respect to x\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}} y = {7x}^{-2}

Awarded Points: 1

Correct Response: \frac{dy}{dx}=-14{x}^{-3}

User Response: \frac{dy}{dx}=-14{x}^{-3}

Differentiate with respect to x\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}} y = {x}^{3}

Awarded Points: 1

Correct Response: \frac{dy}{dx}=3{x}^{2}

User Response: \frac{dy}{dx}=3{x}^{2}

Differentiate with respect to x\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}} y = {x}^{4}

Awarded Points: 1

Correct Response: \frac{dy}{dx}=4{x}^{3}

User Response: \frac{dy}{dx}=4{x}^{3}

Differentiate with respect to x\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}} y = 5x

Awarded Points: 1

Correct Response: \frac{dy}{dx}=5

User Response: \frac{dy}{dx}=5

Differentiate with respect to x\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}} y = 3

Awarded Points: 1

Correct Response: \frac{dy}{dx}=0

User Response: \frac{dy}{dx}=0

Differentiate with respect to x\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}} y = {x}^{2}

Awarded Points: 1

Correct Response: \frac{dy}{dx}=2x

User Response: \frac{dy}{dx}=2x

Differentiate with respect to x\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}} y = 9x

Awarded Points: 1

Correct Response: \frac{dy}{dx}=9

User Response: \frac{dy}{dx}=9

Differentiate with respect to x\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}} y = 6

Awarded Points: 1

Correct Response: \frac{dy}{dx}=0

User Response: \frac{dy}{dx}=0

Differentiate with respect to x\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}} y = {5x}^{4}

Awarded Points: 1

Correct Response: \frac{dy}{dx}=20{x}^{3}

User Response: \frac{dy}{dx}=20{x}^{3}

Differentiate with respect to x\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}} y = -{3x}^{-4}

Awarded Points: 1

Correct Response: \frac{dy}{dx}=12{x}^{-5}

User Response: \frac{dy}{dx}=12{x}^{-5}

Differentiate with respect to x\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}} y = -{3x}^{\frac{1}{2}}

Awarded Points: 1

Correct Response: \frac{dy}{dx}=-\frac{3}{2}{x}^{-\frac{1}{2}}

User Response: \frac{dy}{dx}=-\frac{3}{2}{x}^{-\frac{1}{2}}

Differentiate with respect to x\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}} y = -4{x}^{\frac{2}{3}}

Awarded Points: 1

Correct Response: \frac{dy}{dx}=-\frac{8}{3}{x}^{-\frac{1}{3}}

User Response: \frac{dy}{dx}=-\frac{8}{3}{x}^{-\frac{1}{3}}

Differentiate with respect to x\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}} y = -4{x}^{-\frac{2}{5}}

Awarded Points: 1

Correct Response: \frac{dy}{dx}=\frac{8}{5}{x}^{-\frac{7}{5}}

User Response: \frac{dy}{dx}=\frac{8}{5}{x}^{-\frac{7}{5}}

Differentiate with respect to t\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}} s = -4{t}^{3}-3{t}^{-5}+6{t}^{2}-8t+9

Awarded Points: 1

Correct Response: \frac{ds}{dt}=-12{t}^{2}+15{t}^{-6}+12t-8

User Response: \frac{ds}{dt}=-12{t}^{2}+15{t}^{-6}+12t-8

Differentiate with respect to t\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}} s = \left(2t-3\right)\left(4t-7\right)

Awarded Points: 1

Correct Response: \frac{ds}{dt}=16t-26

User Response: \frac{ds}{dt}=16t-26

Differentiate with respect to t\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}} s = t\left(4{t}^{2}-3{t}^{-6}+6t-8\right)

Awarded Points: 1

Correct Response: \frac{ds}{dt}=12{t}^{2}+15{t}^{-6}+12t-8

User Response: \frac{ds}{dt}=12{t}^{2}+15{t}^{-6}+12t-8

Differentiate with respect to x\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}} s = \frac{4}{\sqrt[3]{x}}

Awarded Points: 1

Correct Response: \frac{ds}{dx}=-\frac{4}{3}{x}^{-\frac{4}{3}}

User Response: \frac{ds}{dx}=-\frac{4}{3}{x}^{-\frac{4}{3}}

Differentiate with respect to x\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}} s = \frac{5+\sqrt{x}}{{x}^{2}}

Awarded Points: 1

Correct Response: \frac{ds}{dx}=-10{x}^{-3}-\frac{3}{2}{x}^{-\frac{5}{2}}

User Response: \frac{ds}{dx}=-10{x}^{-3}-\frac{3}{2}{x}^{-\frac{5}{2}}

C is the curve with equation y= 2{x}^{3}-2{x}^{2}-10x+5\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Use calculus to work out the gradient of C at x=-2.

Awarded Points: 0

Correct Response: 22

User Response: 16

C is the curve with equation y= {x}^{3}-2{x}^{2}-15x+5\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Work out the range of values of x for which C has a negative gradient.

Awarded Points: 0

Correct Response: -\frac{5}{3}<x<3

User Response: \frac{5}{3}<x<-3

A particle moves along a straigh line. \phantom{\rule{0ex}{0ex}}The fixed point O lies on this line.\phantom{\rule{0ex}{0ex}}The displacement of the particle from O at time t seconds, t\ge 0, is s metres, where\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}} s = {t}^{3}-5{t}^{2}-8t+3\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Find the value of t for which the particle is ins\mathrm{tan}\mathrm{tan}eously at rest.

Responses

Awarded Points: 1

Correct Response: \frac{dy}{dx}=12x

User Response: \frac{dy}{dx}=12x

Awarded Points: 1

Correct Response: \frac{dy}{dx}=-14{x}^{-3}

User Response: \frac{dy}{dx}=-14{x}^{-3}

Awarded Points: 1

Correct Response: \frac{dy}{dx}=3{x}^{2}

User Response: \frac{dy}{dx}=3{x}^{2}

Awarded Points: 1

Correct Response: \frac{dy}{dx}=4{x}^{3}

User Response: \frac{dy}{dx}=4{x}^{3}

Awarded Points: 1

Correct Response: \frac{dy}{dx}=5

User Response: \frac{dy}{dx}=5

Awarded Points: 1

Correct Response: \frac{dy}{dx}=0

User Response: \frac{dy}{dx}=0

Awarded Points: 1

Correct Response: \frac{dy}{dx}=2x

User Response: \frac{dy}{dx}=2x

Awarded Points: 1

Correct Response: \frac{dy}{dx}=9

User Response: \frac{dy}{dx}=9

Awarded Points: 1

Correct Response: \frac{dy}{dx}=0

User Response: \frac{dy}{dx}=0

Awarded Points: 1

Correct Response: \frac{dy}{dx}=20{x}^{3}

User Response: \frac{dy}{dx}=20{x}^{3}

Awarded Points: 1

Correct Response: \frac{dy}{dx}=12{x}^{-5}

User Response: \frac{dy}{dx}=12{x}^{-5}

Awarded Points: 1

Correct Response: \frac{dy}{dx}=-\frac{3}{2}{x}^{-\frac{1}{2}}

User Response: \frac{dy}{dx}=-\frac{3}{2}{x}^{-\frac{1}{2}}

Awarded Points: 1

Correct Response: \frac{dy}{dx}=-\frac{8}{3}{x}^{-\frac{1}{3}}

User Response: \frac{dy}{dx}=-\frac{8}{3}{x}^{-\frac{1}{3}}

Awarded Points: 1

Correct Response: \frac{dy}{dx}=\frac{8}{5}{x}^{-\frac{7}{5}}

User Response: \frac{dy}{dx}=\frac{8}{5}{x}^{-\frac{7}{5}}

Awarded Points: 1

Correct Response: \frac{ds}{dt}=-12{t}^{2}+15{t}^{-6}+12t-8

User Response: \frac{ds}{dt}=-12{t}^{2}+15{t}^{-6}+12t-8

Awarded Points: 1

Correct Response: \frac{ds}{dt}=16t-26

User Response: \frac{ds}{dt}=16t-26

Awarded Points: 1

Correct Response: \frac{ds}{dt}=12{t}^{2}+15{t}^{-6}+12t-8

User Response: \frac{ds}{dt}=12{t}^{2}+15{t}^{-6}+12t-8

Awarded Points: 1

Correct Response: \frac{ds}{dx}=-\frac{4}{3}{x}^{-\frac{4}{3}}

User Response: \frac{ds}{dx}=-\frac{4}{3}{x}^{-\frac{4}{3}}

Awarded Points: 1

Correct Response: \frac{ds}{dx}=-10{x}^{-3}-\frac{3}{2}{x}^{-\frac{5}{2}}

User Response: \frac{ds}{dx}=-10{x}^{-3}-\frac{3}{2}{x}^{-\frac{5}{2}}

Awarded Points: 0

Correct Response: 22

User Response: 16

Awarded Points: 0

Correct Response: -\frac{5}{3}<x<3

User Response: \frac{5}{3}<x<-3

Awarded Points: 1

Correct Response: t=4

User Response: t=4