(a) Show that for real constants and , the derivative of with respect to is . (b)…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

(a) Show that for real constants aa and bb, the derivative of cos⁡(ax+b)\cos(ax+b) with respect to xx is −asin⁡(ax+b)-a\sin(ax+b). (b) Using the result from part (a), find ddx cos⁡(7x−5)\dfrac{d}{dx}\,\cos(7x-5). (c) Verify your answer in part (b) by evaluating both the derivative formula and the numerical derivative at x=π7x=\dfrac{\pi}{7} and showing that they agree.

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