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Popular >

derivative of xsqrt(36-x^2)

Solution

\frac{d}{d x} (x 36 - x^{2})

Solution

\frac{- 2 x ^{2} + 36}{36 - x ^{2}}

Solution steps

\frac{d}{d x} (x 36 - x^{2})

Apply the Product Rule:

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

f = x, g = 36 - x^{2}

= \frac{d x}{d x} 36 - x^{2} + \frac{d}{d x} (36 - x^{2}) x

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

\frac{d}{d x} (36 - x^{2}) = - \frac{x}{36 - x ^{2}}

= 1 \cdot 36 - x^{2} + (- \frac{x}{36 - x ^{2}}) x

Simplify

1 \cdot 36 - x^{2} + (- \frac{x}{36 - x ^{2}}) x : \frac{- 2 x ^{2} + 36}{36 - x ^{2}}

= \frac{- 2 x ^{2} + 36}{36 - x ^{2}}

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\int \frac{x ^{3}}{3 x} d x

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x \to 2 lim (\frac{f ( x )}{g ( x )})

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\int \frac{( x ^{2} - x + 6 )}{( x ^{3} - 3 x )} d x

Frequently Asked Questions (FAQ)

What is the derivative of xsqrt(36-x^2) ?
The derivative of xsqrt(36-x^2) is (-2x^2+36)/(sqrt(36-x^2))
What is the first derivative of xsqrt(36-x^2) ?
The first derivative of xsqrt(36-x^2) is (-2x^2+36)/(sqrt(36-x^2))