Question

How do you find the derivative of `y=10tan(20x)`?

Answer 1

`dy/dx=200sec^2(20)x`

Explanation:

First we need to find the derivative of `Tan ax` where a is constant
`y = tanax`
`dy/dx=d/dx((sinax)/(cosax))`
applying `u/v` rule
where `u=sinax,v=cosax`
`dy/dx`=`(1/(cos^2ax))``(cosax``(d/dx(sinax))`-`sinax(d/dx(cosax))`
`dy/dx`=`(1/(cos^2ax))`*`(cosax*acosx)`-`sinax*(-asinax))`
`dy/dx`=`a(sin^2ax+cos^2ax)/(cos^2ax)`=`a/(cos^2ax)`
`dy/dx`=`asec^2ax`
so as in the problem y = 10 tan 20x
the answer is `dy/dx=10*20*sec^2(10x)=200sec^2(20x)`