Find the Derivative - d/dx sin(x^5)

Problem

d(sin(x5))/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=x5

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

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

4. Differentiate the inner function with respect to x The derivative of x5 using the Power Rule is 5*x4

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

Final Answer

d(sin(x5))/d(x)=5*x4*cos(x5)

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