Calculating Derivative – A function with square root and a parameter – Exercise 6345

Exercise

Find the derivative of the following function:

f(x)=\sqrt{r^2-x^2}

with parameter r.

Final Answer

Show final answer

Solution

f(x)=\sqrt{r^2-x^2}

Using Derivative formulas and the chain rule in Derivative Rules, we get the derivative:

f'(x)=\frac{1}{2\sqrt{r^2-x^2}}\cdot (-2x)=

One can simplify the derivative:

=\frac{-x}{\sqrt{r^2-x^2}}

Have a question? Found a mistake? – Write a comment below!
Was it helpful? You can buy me a cup of coffee here, which will make me very happy and will help me upload more solutions!