Question

Differenciate sinx to the power 5?

Answer 1

Shown below

Explanation:

Use the chain rule:

`d/dx f ( g(x) ) = f'(g(x) ) * g'(x)`

`=> d/dx sin^5 x = d/dx ( sinx )^5`

`=> 5 sin^4 x * d/dx sinx`

`= 5 cosx sin^4 x`

Answer 2

`5cosxsin^4x`

Explanation:

`"differentiate using the "color(blue)"chain rule"`

`"given "y=f(g(x))" then"`

`dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"`

`"here "y=sin^5x=(sinx)^5`

`rArrdy/dx=5(sinx)^4xxd/dx(sinx)`

`color(white)(rArrdy/dx)=5cosxsin^4x`