Alright, lets get started.
The given equation is :
[tex]y =tan (5t)[/tex]
Differentiating with respect of t
[tex]\frac{dy}{dt}=\frac{d}{dt}tan(5t)[/tex]
Derivative of tan is [tex]sec^{2}[/tex]
But here we have tan (5t), so we have too use chain rule here
[tex]\frac{dy}{dt}=\frac{d}{dt}(5t)*sec^{2} (5t)[/tex]
[tex]\frac{dy}{dt}= 5*sec^{2}(5t)[/tex]
[tex]\frac{dy}{dt}= 5sec^{2}(5t)[/tex] : Answer
Hope it will help :)
