Question

If $z=x{e}^y,x=t$ and $y=1+3t$, then $\frac{dz}{dt}$ is equal to

• A. $e^y.3t$
• B. $xz$
• C. $e^y(1+3t)$
• D. $xyz$

Answer 1

Answer: (C)

$e^y(1+3t)$

The given information in the question is:

$z=x{e}^y$, $x=t$ and $y=1+3t$

Subsitituting the value of x and y in z we get,

$\Rightarrow z=t{e}^{1+3t}$

$\Rightarrow z=et{e}^{3t}$

Now finding the first derivative of the function z w.r.t. to t we get,

$\Rightarrow \frac{dz}{dt}=e(e^{3t}+3t{e}^{3t})$

$\Rightarrow \frac{dz}{dt}=e^{1+3t}(1+3t)$

$\Rightarrow \frac{dz}{dt}=e^y(1+3t)$