The temperature in degrees Celsius at a point on a metal rod depends on the distance…

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

The temperature

T

in degrees Celsius at a point on a metal rod depends on the distance

x

in centimeters from one end according to

T=5x^{2}+20

. If

x

is itself a differentiable function of time

t

(measured in seconds), which of the following expressions correctly represents

\dfrac{dT}{dt}

in terms of

x

and

\dfrac{dx}{dt}

? (a)

5x\,\dfrac{dx}{dt}

(b)

10x\,\dfrac{dx}{dt}

(c)

10x

(d)

10\,\dfrac{dx}{dt}