What is the derivative of sin^4(tan5x)

Question

Finding derivative of sin^4(tan5x)

Answer 1

f(x) = sin⁴(tan5x)

 

Use the power rule, chain rule, quotient rule, and chain rule again.

 

f'(x) = 4sin³(tan5x) cos(tan5x) {[cos²5x - (-sin²5x)]/cos²5x}(5)

 

Note that 

 

cos²5x - (-sin²5x) = 1 ⇒

 

f'(x) = 20sin³(tan5x) cos(tan5x) / cos²5x