Find the Derivative - d/d@VAR f(x)=(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 part of the expression. Bring the exponent 2 down and multiply it by the constant 16

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. Combine the results and simplify the coefficients.

32*(3*x2−7*x−3)*(6*x−7)

5. Distribute the constant 32 into one of the binomials to reach the final simplified form.

(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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