Question

What is the derivative of `tan^2(sinx)`?

Answer 1

`"d"/("d"x) tan^2(sin(x)) = 2tan(sin(x))sec^2(sin(x))cos(x)`

Explanation:

By the chain rule,

`"d"/("d"x) tan^2(sin(x)) = 2*tan(sin(x))* "d"/("d"x) (tan(sin(x)))`,
`"d"/("d"x) tan^2(sin(x)) = 2tan(sin(x))sec^2(sin(x))*"d"/("d"x)(sin(x))`,
`"d"/("d"x) tan^2(sin(x)) = 2tan(sin(x))sec^2(sin(x))cos(x)`.