Chapter 3.4, Problem 1E

To determine

To find: The derivative of the function $f\left(x\right)=4\cos x$ .

Answer to Problem 1E

  $-4\sin x$

Explanation of Solution

Given:

  $f\left(x\right)=4\cos x$

Formula used:

  $\frac{d}{dx}\left(\cos x\right)=-\sin x$

Calculation:

Differentiate the given function with respect to x.

  $\begin{array}{c}\frac{d}{dx}\left(f\left(x\right)\right)=\frac{d}{dx}\left(4\cos x\right)\\ =4\frac{d}{dx}\left(\cos x\right)\\ =4\left(-\sin x\right)\\ =-4\sin x\end{array}$

Conclusion:

  $\frac{d}{dx}\left(f\left(x\right)\right)=-4\sin x$