Question

Derivative of tan^2 x

Answer 1

`2sec^2xtanx`

Explanation:

`(d)/(dx) tan^2x`

`(d)/(dx) tanxtanx`

`((d)/(dx)tanx)(tanx)+(tanx)((d)/(dx)tanx)`

`(d)/(dx)tanx=(d)/(dx)(sinx)/(cosx)=((cosx)(cosx)-(sinx)(-sinx))/((cosx)^2)=(cos^2x+sin^2x)/(cos^2x)=(1)/(cos^2x)=sec^2x`

`(sec^2x)(tanx)+(tanx)(sec^2x)`

`2sec^2xtanx`

Helpful tips:

Product Rule:
`(d)/(dx)f(x)g(x)=f'(x)g(x)+f(x)g'(x)=(d)/(dx)f(x)*g(x)+f(x)*(d)/(dx)g(x)`

Quotient Rule:
`(d)/(dx)(f(x))/(g(x))=(g(x)f'(x)-f(x)g'(x))/((g(x))^2)=(g(x)(d)/(dx)f(x)-f(x)(d)/(dx)g(x))/((g(x))^2)`

Pythagorean Identity:
`cos^2x+sin^2x=1`