Question

Find the differential of each function. (a) y = tan (5t)

Answer 1

Alright, lets get started.

The given equation is :

$y =tan (5t)$

Differentiating with respect of t

$\frac{dy}{dt}=\frac{d}{dt}tan(5t)$

Derivative of tan is $sec^{2}$

But here we have tan (5t), so we have too use chain rule here

$\frac{dy}{dt}=\frac{d}{dt}(5t)*sec^{2} (5t)$

$\frac{dy}{dt}= 5*sec^{2}(5t)$

$\frac{dy}{dt}= 5sec^{2}(5t)$   :    Answer

Hope it will help :)