Chapter 3 - Section 3.3 - Derivatives of Trigonometric Functions - 3.3 Exercises - Page 198: 34

See image. a) $f'(x)=(e^x)\frac{1}{dx}\cos(x)+e^x(\cos(x))\frac{1}{dx}$ $=e^x\cos(x)-e^x\sin(x)$ $f''(x)=e^x\cos(x)-e^x\sin(x)-e^x\sin(x)-e^x\cos(x)=-2e^x\sin(x)$ b) The x value of the maximum point on $f(x)$ is an x intercept of $f'(x)$ and the x value of the maximum point on $f'(x)$ is an x intercept of $f''(x)$, so the derivatives are reasonable

a) $f'(x)=(e^x)\frac{1}{dx}\cos(x)+e^x(\cos(x))\frac{1}{dx}$ $=e^x\cos(x)-e^x\sin(x)$ $f''(x)=e^x\cos(x)-e^x\sin(x)-e^x\sin(x)-e^x\cos(x)=-2e^x\sin(x)$ b) The x value of the maximum point on $f(x)$ is an x intercept of $f'(x)$ and the x value of the maximum point on $f'(x)$ is an x intercept of $f''(x)$, so the derivatives are reasonable