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

Problem

d()/d(x)*(x2−9)2

Solution

1. Identify the outer function and the inner function to apply the Chain Rule, where the outer function is u2 and the inner function is u=x2−9

2. Apply the Chain Rule by taking the derivative of the outer function with respect to the inner function and multiplying it by the derivative of the inner function.

d(x2−9)/d(x)=2*(x2−9)⋅d(x2−9)/d(x)

3. Differentiate the inner expression x2−9 using the Power Rule.

d(x2−9)/d(x)=2*x

4. Substitute the derivative of the inner expression back into the equation.

d(x2−9)/d(x)=2*(x2−9)*(2*x)

5. Simplify the expression by multiplying the terms.

d(x2−9)/d(x)=4*x*(x2−9)

Final Answer

d(x2−9)/d(x)=4*x3−36*x

Want more problems? Check here!