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Popular Calculus >

derivative of xsqrt(25-x^2)

Solution

\frac{d}{d x} (x 25 - x^{2})

Solution

\frac{- 2 x ^{2} + 25}{25 - x ^{2}}

Solution steps

\frac{d}{d x} (x 25 - x^{2})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 25 - x^{2}

= \frac{d x}{d x} 25 - x^{2} + \frac{d}{d x} (25 - x^{2}) x

\frac{d x}{d x} = 1

\frac{d}{d x} (25 - x^{2}) = - \frac{x}{25 - x ^{2}}

= 1 \cdot 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x

Simplify

1 \cdot 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x : \frac{- 2 x ^{2} + 25}{25 - x ^{2}}

= \frac{- 2 x ^{2} + 25}{25 - x ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of xsqrt(25-x^2) ?
The derivative of xsqrt(25-x^2) is (-2x^2+25)/(sqrt(25-x^2))
What is the first derivative of xsqrt(25-x^2) ?
The first derivative of xsqrt(25-x^2) is (-2x^2+25)/(sqrt(25-x^2))