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

Answer 1

Elijah Abram

Read below.

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)#

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Answer 2

Cameron Alexander

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

#"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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Answer 3

Elijah Abram

To differentiate ( f(x) = \sin(x^3) ), you can use the chain rule. The derivative is ( f'(x) = 3x^2 \cos(x^3) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.