Find the Derivative - d/dx (x^2+4)^5

Problem

d(x^2+4)/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule, where the outer function is u^5 and the inner function is u=x^2+4

2. Apply the Power Rule to the outer function by bringing the exponent down and subtracting one from the power.

5*(x^2+4)^4

3. Multiply by the derivative of the inner function x^2+4 with respect to x

5*(x^2+4)^4⋅d(x^2+4)/d(x)

4. Differentiate the inner expression using the Power Rule for x^2 and the Constant Rule for 4

d(x^2+4)/d(x)=2*x

5. Simplify the expression by multiplying the terms together.

5*(x^2+4)^4⋅2*x=10*x*(x^2+4)^4

Final Answer

d(x^2+4)/d(x)=10*x*(x^2+4)^4

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