Differenciate sinx to the power 5?

2 Answers
Rhys
May 6, 2018

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 #

Jim G.
May 6, 2018

#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#

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