How do you find the derivative of ${cos}^{6} (2 x + 5)$ $cos^6(2x+5)$ ?

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Answer 1 · 2018-06-24T21:36:01

Applying chain rule for differentiation as follows

$\frac{d}{d x} {cos}^{6} (2 x + 5)$ $\frac{d}{dx}\cos^6(2x+5)$

$= \frac{d}{d x} {(cos (2 x + 5))}^{6}$ $=\frac{d}{dx}(\cos(2x+5))^6$

$= 6 {(cos (2 x + 5))}^{5} \frac{d}{d x} (cos (2 x + 5))$ $=6(\cos(2x+5))^5\frac{d}{dx}(\cos(2x+5))$

$= 6 {cos}^{5} (2 x + 5) (- sin (2 x + 5)) \frac{d}{d x} (2 x + 5)$ $=6\cos^5(2x+5)(-\sin(2x+5))\frac{d}{dx}(2x+5)$

$= - 6 sin (2 x + 5) {cos}^{5} (2 x + 5) (2)$ $=-6\sin(2x+5)\cos^5(2x+5)(2)$

$= - 12 sin (2 x + 5) {cos}^{5} (2 x + 5)$ $=-12\sin(2x+5)\cos^5(2x+5)$

How do you find the derivative of cos^6(2x+5)cos6(2x+5)cos^6(2x+5)?