Question

Let $f$ be a real valued function such that $f=v o u$ and $t=u(x)$. If $\frac{d t}{d x} \cdot \frac{d u}{d t}$ exists, then

• A. $\frac{d f}{d u}=\frac{d t}{d v} \cdot \frac{d t}{d u}$
• B. $\frac{d f}{d u}=\frac{d u}{d t} \cdot \frac{d x}{d t}$
• C. $\frac{d f}{d x}=\frac{d u}{d t} \cdot \frac{d t}{d x}$
• 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., $f=v o u$. Suppose $t=u(x)$ and if both $\frac{d t}{d x}$ and $\frac{d v}{d t}$ exist, we have
$\frac{d f}{d x}=\frac{d v}{d t} \cdot \frac{d t}{d x}$