Question

1. - / 5.26 points find the derivative of the function. y = a^7 + cos^7 x y(x) =

Explanation:

Step1: Differentiate constant term

Derivative of \(a^7\) (constant) is 0.

Step2: Differentiate \(\cos^7 x\) via chain rule

Let \(u = \cos x\), so \(\frac{du}{dx} = -\sin x\). Then \(\frac{d}{du}(u^7) = 7u^6\). Multiply: \(7\cos^6 x(-\sin x)\).

Step3: Combine results

Add derivatives of both terms.

Answer:

\(7\cos^6 x(-\sin x)\) or \(-7\cos^6 x \sin x\)