Question

Let $f$ be a real valued function such that $f=vou$ and $t=u(x)$. If $\frac{dt}{dx}\cdot \frac{du}{dt}$ exists, then

• A. $\frac{df}{du}=\frac{dt}{dv}\cdot \frac{dt}{du}$
• B. $\frac{df}{du}=\frac{du}{dt}\cdot \frac{dx}{dt}$
• C. $\frac{df}{dx}=\frac{du}{dt}\cdot \frac{dt}{dx}$
• D. None of these

Answer 1

Answer: (C)

Let $f$ be a real valued function which is a composite of two functions $u$ and $v$ i.e., $f=vou$. Suppose $t=u(x)$ and if both $\frac{dt}{dx}$ and $\frac{dv}{dt}$ exist, we have
$\frac{df}{dx}=\frac{dv}{dt}\cdot \frac{dt}{dx}$