Find the Derivative - d/dx y=(2x^3+9x)^5

Problem

d()/d(x)*(2*x^3+9*x)^5

Solution

1. Identify the outer function and the inner function to apply the Chain Rule.

2. Apply the Chain Rule by taking the derivative of the outer function u^5 with respect to u where u=2*x^3+9*x

3. Differentiate the inner function 2*x^3+9*x with respect to x

4. Multiply the derivative of the outer function by the derivative of the inner function.

5. Simplify the resulting expression.

Final Answer

d(2*x^3+9*x)/d(x)=5*(2*x^3+9*x)^4*(6*x^2+9)

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