Question

\(\dfrac{d}{dx}\big(e^{x}+\cos5x\big)=\) ?

• A. \(e^{x}=\cos5x\)
• B. \(e^{x}+5\sin5x\)
• C. \(e^{x}-5\sin5x\)
• D. \(e^{x}-5\cos5x\)

Hint:

For $\cos(kx)$, derivative is $-k\sin(kx)$.

Answer 1

The Correct Option is C

Differentiate termwise: \(\dfrac{d}{dx}(e^{x})=e^{x}\); \(\dfrac{d}{dx}(\cos5x)=-\sin5x\cdot 5\) by chain rule. Add: \[ e^{x}-5\sin5x. \]