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

Problem

d(cos(x3))/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is cos(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 cos(u) with respect to u which results in −sin(u)

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

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

6. Simplify the expression by rearranging the terms.

Final Answer

d(cos(x3))/d(x)=−3*x2*sin(x3)

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