Question

How do you find the derivative of `y=tan^2(5x)`?

Answer 1

`dy/dx=10tan5xsec^2 5x`

Explanation:

`"differentiate using the "color(blue)"chain rule"`

`"Given "y=f(g(x))" then"`

`dy/dx=f'(g(x))xxg'(x)`

`y=tan^2 5x=(tan5x)^2`

`rArrdy/dx=2tan5x xxd/dx(tan5x)`

`color(white)(rArrdy/dx)=2tan5x xxsec^2 5x xxd/dx(5x)`

`color(white)(rArrdy/dx)=10tan5xsec^2 5x`