Find the Derivative - d/dx y=(6x+3)^4

Problem

d()/d(x)*(6*x+3)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=6*x+3

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

d(y)/d(x)=4*(6*x+3)(4−1)⋅d(6*x+3)/d(x)

3. Differentiate the inner function 6*x+3 with respect to x

d(6*x+3)/d(x)=6

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

d(y)/d(x)=4*(6*x+3)3⋅6

5. Simplify the expression by multiplying the constants.

d(y)/d(x)=24*(6*x+3)3

Final Answer

d()/d(x)*(6*x+3)4=24*(6*x+3)3

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