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Popular >

derivative of xsqrt(100-x^2)

Solution

\frac{d}{d x} (x 100 - x^{2})

Solution

\frac{- 2 x ^{2} + 100}{100 - x ^{2}}

Solution steps

\frac{d}{d x} (x 100 - x^{2})

Apply the Product Rule:

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

f = x, g = 100 - x^{2}

= \frac{d x}{d x} 100 - x^{2} + \frac{d}{d x} (100 - x^{2}) x

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

\frac{d}{d x} (100 - x^{2}) = - \frac{x}{100 - x ^{2}}

= 1 \cdot 100 - x^{2} + (- \frac{x}{100 - x ^{2}}) x

Simplify

1 \cdot 100 - x^{2} + (- \frac{x}{100 - x ^{2}}) x : \frac{- 2 x ^{2} + 100}{100 - x ^{2}}

= \frac{- 2 x ^{2} + 100}{100 - x ^{2}}

Graph

Popular Examples

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\int \frac{1}{x ^{5}} - \frac{1}{x} d x

x^{''}-8x^'+17x=0

x^{^{''}} - 8 x^{^{'}} + 17 x = 0

derivative of e^{x/((x-6)})

\frac{d}{d x} (e^{\frac{x}{( x - 6 )}})

derivative of ln(1-3/x)

\frac{d}{d x} (ln (1 - \frac{3}{x}))

limit as x approaches 2 of (x^2-2x)/x

x \to 2 lim (\frac{x ^{2} - 2 x}{x})

Frequently Asked Questions (FAQ)

What is the derivative of xsqrt(100-x^2) ?
The derivative of xsqrt(100-x^2) is (-2x^2+100)/(sqrt(100-x^2))
What is the first derivative of xsqrt(100-x^2) ?
The first derivative of xsqrt(100-x^2) is (-2x^2+100)/(sqrt(100-x^2))