Let be the temperature (in °C) of a solution

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let

T

be the temperature (in °C) of a solution, which is a differentiable function of its volume

V

(in liters). The volume

V

is, in turn, a differentiable function of time

t

(in seconds). Which of the following correctly expresses

\dfrac{dT}{dt}

in terms of

\dfrac{dT}{dV}

and

\dfrac{dV}{dt}

? (a)

-\dfrac{dT}{dV}\,\dfrac{dV}{dt}

(b)

\displaystyle \frac{dT}{dV}\,\frac{dV}{dt}

(c)

\displaystyle \frac12\,\frac{dT}{dV}\,\frac{dV}{dt}

(d)

\displaystyle 2\,\frac{dT}{dV}\,\frac{dV}{dt}