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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


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

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}}

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