Find the Derivative - d/dx g(x)=2(4-7x)^4

Problem

d()/d(x)*2*(4−7*x)4

Solution

1. Identify the constant multiple rule, which allows the constant 2 to be moved outside the derivative.

(d(2)*(4−7*x)4)/d(x)=2d(4−7*x)/d(x)

2. Apply the power rule and the chain rule to the expression (4−7*x)4

d(4−7*x)/d(x)=4*(4−7*x)3⋅d(4−7*x)/d(x)

3. Differentiate the inner function 4−7*x with respect to x

d(4−7*x)/d(x)=−7

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

2⋅4*(4−7*x)3⋅(−7)

5. Simplify the expression by multiplying the numerical constants 2 4 and −7

2⋅4⋅(−7)=−56

Final Answer

(d(2)*(4−7*x)4)/d(x)=−56*(4−7*x)3

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