Chapter 3.1, Problem 33E

To determine

To calculate:The one sided derivatives of the function $f\left(x\right)$ .

Answer to Problem 33E

The derivative of $\sin x$ is $\cos x$ .

Explanation of Solution

Given information:

  $y=\sin x$

  $x=\cos x$

Formula used:

  $\frac{d}{dx}f\left(x\right)=f\text{'}\left(x\right)$

Where $f\left(x\right)$ is the function and $h$ is a constant.

Calculation:

The cosine function is the derivatives of the sine function.

At the increasing value of sine the values of the cosine are positive.

At the peak value of sine function, cosine is zero.

Similarly at the decreasing value of the sine function, cosine function will be negative.

  

Now, find the derivatives, use the formula $\frac{d}{dx}f\left(x\right)=f\text{'}\left(x\right)$ .

  $\frac{d}{dx}\sin x=\cos x$

Similarly, $\frac{d}{dx}\cos x=-\sin x$

Hence, the derivative of $\sin x$ is $\cos x$ .