Find the Derivative - d/dx sin(x^4)

Problem

d(sin(x4))/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=x4

2. Apply the Chain Rule which states that the derivative of ƒ*(g(x)) is ƒ′*(g(x))⋅g(x)′

3. Differentiate the outer function with respect to the inner function. The derivative of sin(u) is cos(u)

cos(x4)

4. Differentiate the inner function with respect to x The derivative of x4 using the Power Rule is 4*x3

d(x4)/d(x)=4*x3

5. Multiply the results of the derivatives together to find the final derivative.

cos(x4)⋅4*x3

Final Answer

d(sin(x4))/d(x)=4*x3*cos(x4)

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