Find the Derivative - d/dx (x^3-8)^4

Problem

d()/d(x)*(x3−8)4

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is u4 and the inner function is u=x3−8

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

d()/d(x)*(x3−8)4=4*(x3−8)3⋅d()/d(x)*(x3−8)

3. Differentiate the inner function x3−8 using the Power Rule.

d()/d(x)*(x3−8)=3*x2

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

4*(x3−8)3⋅3*x2

5. Simplify the expression by multiplying the constants and terms outside the parentheses.

12*x2*(x3−8)3

Final Answer

d()/d(x)*(x3−8)4=12*x2*(x3−8)3

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