Question

1. - / 5.26 points

find the derivative of the function.
y = cos(a⁹ + x⁹)
y’(x) =

Explanation:

Step1: Apply chain rule

Let $u = a^9 + x^9$, so $y = \cos(u)$. The derivative of $\cos(u)$ is $-\sin(u)$.

Step2: Differentiate inner function

$\frac{du}{dx} = 9x^8$ (since $a^9$ is constant).

Step3: Multiply derivatives

$y'(x) = -\sin(u) \cdot \frac{du}{dx} = -\sin(a^9 + x^9) \cdot 9x^8$

Answer:

$-9x^8\sin(a^9 + x^9)$