Find the Derivative - d/dx sin(x^3)

Problem

d(sin(x3))/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is sin(u) and the inner function is u=x3

2. Apply the Chain Rule which states that (d(ƒ)*(g(x)))/d(x)=ƒ′*(g(x))⋅g(x)′

3. Differentiate the outer function sin(u) with respect to u which results in cos(u)

4. Differentiate the inner function x3 with respect to x using the Power Rule, which results in 3*x2

5. Multiply the results together and substitute x3 back in for u

Final Answer

d(sin(x3))/d(x)=3*x2*cos(x3)

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