Find the Derivative - d/dx (3x^2-7x-3)^2*16

Problem

d()/d(x)*(3*x2−7*x−3)2⋅16

Solution

1. Identify the constant and the outer function. The constant 16 can be moved outside the derivative, and the expression (3*x2−7*x−3)2 requires the power rule and the chain rule.

2. Apply the power rule to the outer function. Bring the exponent 2 to the front and decrease the power by 1

16⋅2*(3*x2−7*x−3)(2−1)⋅d(3*x2−7*x−3)/d(x)

3. Differentiate the inner function 3*x2−7*x−3 using the power rule for each term.

d(3*x2−7*x−3)/d(x)=6*x−7

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

32*(3*x2−7*x−3)*(6*x−7)

5. Simplify by multiplying the constant 32 into one of the binomial factors.

(3*x2−7*x−3)*(192*x−224)

Final Answer

d()/d(x)*(3*x2−7*x−3)2⋅16=(3*x2−7*x−3)*(192*x−224)

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