Find the Derivative - d/dx 3(4-9x)^4

Problem

d()/d(x)*3*(4−9*x)4

Solution

1. Identify the constant multiple rule, which allows the constant 3 to be moved outside the derivative.

d()/d(x)*3*(4−9*x)4=3⋅d(4−9*x)/d(x)

2. Apply the power rule and the chain rule to the expression (4−9*x)4 where the outer function is u4 and the inner function is u=4−9*x

d(4−9*x)/d(x)=4*(4−9*x)3⋅d(4−9*x)/d(x)

3. Differentiate the inner function 4−9*x with respect to x

d(4−9*x)/d(x)=−9

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

3⋅4*(4−9*x)3⋅(−9)

5. Simplify the expression by multiplying the numerical constants 3 4 and −9

3⋅4⋅(−9)=−108

Final Answer

(d(3)*(4−9*x)4)/d(x)=−108*(4−9*x)3

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