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

2 Answers
Parabola
Apr 19, 2018

Read below.

Explanation:

We use the chain rule:

#d/dx[f(g(x))]=f'(g(x))*g'(x)#

Power rule:

#d/dx[x^n]=nx^(n-1)#

#d/dx[sinx]=cosx#

Therefore:

#f'(x)=cos(x^3)*d/dx[x^3]#

#=>f'(x)=cos(x^3)*3x^(3-1)#

#=>f'(x)=3x^2cos(x^3)#

Jim G.
Apr 19, 2018

#3x^2cos(x^3)#

Explanation:

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

#"Given "f(x)=g(h(x))" then"#

#f'(x)=g'(h(x))xxg'(x)larrcolor(blue)"chain rule"#

#f(x)=sin(x^3)#

#rArrf'(x)=cos(x^3)xxd/dx(x^3)=3x^2cos(x^3)#

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