Questiondifferentiats $$\cos ^{x}$$

Studdy Solution
Solve for $\frac{dy}{dx}$ by multiplying both sides by $y$:
$$\frac{dy}{dx} = y \left(-x \tan(x) + \ln(\cos(x))\right)$$
Substitute back $y = (\cos(x))^x$:
$$\frac{dy}{dx} = (\cos(x))^x \left(-x \tan(x) + \ln(\cos(x))\right)$$
The derivative of $y = \cos^x$ is:
$$\frac{dy}{dx} = (\cos(x))^x \left(-x \tan(x) + \ln(\cos(x))\right)$$