Differentiate w=(tan(x)+cos(4x))^3

Question

I just dont know how to do it.

Answer 1

Use the power rule, the chain rule, and the sum rule.

 

Recall that 

 

[tan(x)]' = 1/cos²x

 

[cos(ax)]' = -a sin(ax)

 

Then

 

dw/dx = 3([tan(x) + cos(4x)]² [1/cos²(x) - 4sin(4x)]