Question

How do you differentiate `f(x)=(sin(tanx))^3`?

Answer 1

`dy/dx=3sec^2x*cos(tanx)(sin(tanx))^2`

Explanation:

Begin by differentiating the outermost part of the function:

`dy/dx=3(sin(tanx))^2*d/dx(sin(tanx))`

Because this is a composition of functions, we must use the chain rule to differentiate the inner function.

Simplifying we get:

`dy/dx=3(sin(tanx))^2cos(tanx)*d/dx(tanx)`

`sin(tanx)` is again a composition of functions, so we must use the chain rule one more time.

Simplifying gives the final answer:

`dy/dx=3sec^2x*cos(tanx)(sin(tanx))^2`

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