Question

What is the derivative of `tan^5(x)`?

Answer 1

`y=tan^5x=(tanx)^5=>dy/dx=5(tanx)^4d/(dx)(tanx)`
`=>dy/dx=5tan^4x*sec^2x`

Explanation:

Let,
`y=tan^5x=(tanx)^5`
We take,
`y=u^5,` where, `u=tanx`
`=>(dy)/(du)=5u^4 and (du)/(dx)=sec^2x`
Applying chain rule
`dy/dx=dy/(du)*(du)/dx`
`=>dy/dx=5u^4*sec^2x`
`=>dy/dx=5(tanx)^4*sec^2x`
`=>dy/dx=5tan^4xsec^2x`