How do you find the derivative of ${cos}^{5} (w) \cdot 6 cos (w^{5})$ $cos^5(w)*6cos(w^5)$ ?

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How do you find the derivative of ${cos}^{5} (w) \cdot 6 cos (w^{5})$ $cos^5(w)*6cos(w^5)$ ?

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Answer 1 · 2018-06-02T08:47:32

$- 30 sin (w) \cdot {cos}^{4} (w) \cdot cos (w^{5}) - 30 \cdot sin (w^{5}) \cdot {cos}^{5} (w) \cdot w^{4}$ $-30sin(w)*cos^4(w)*cos(w^5)-30*sin(w^5)*cos^5(w)*w^4$

Explanation:

Using the product rule and the chain rule we get

$5 {cos}^{4} (w) \cdot (- sin (w)) \cdot 6 \cdot cos (w^{5}) + {cos}^{5} (w) \cdot 6 \cdot (- sin (w^{5})) \cdot 5 w^{4}$ $5cos^4(w)*(-sin(w))*6*cos(w^5)+cos^5(w)*6*(-sin(w^5))*5w^4$

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How do you find the derivative of ${cos}^{5} (w) \cdot 6 cos (w^{5})$ $cos^5(w)*6cos(w^5)$ ?

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How do you find the derivative of ${cos}^{5} (w) \cdot 6 cos (w^{5})$ $cos^5(w)*6cos(w^5)$ ?