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Popular >

derivative of (x^2/(7+x))

Solution

\frac{d}{d x} (\frac{x ^{2}}{7 + x})

Solution

\frac{14 x + x ^{2}}{( 7 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{7 + x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{2} ) ( 7 + x ) - \frac{d}{d x} ( 7 + x ) x ^{2}}{( 7 + x ) ^{2}}

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

\frac{d}{d x} (7 + x) = 1

= \frac{2 x ( 7 + x ) - 1 \cdot x ^{2}}{( 7 + x ) ^{2}}

Simplify

\frac{2 x ( 7 + x ) - 1 \cdot x ^{2}}{( 7 + x ) ^{2}} : \frac{14 x + x ^{2}}{( 7 + x ) ^{2}}

= \frac{14 x + x ^{2}}{( 7 + x ) ^{2}}

Popular Examples

derivative of (x^2+6)/x derivative of

\frac{x ^{2} + 6}{x}

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\int \frac{2 x ^{3} - x ^{2} + 4 x - 4}{x ^{4} - 4 x ^{2}} d x

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\int_{0}^{2} 1 0^{x} d x

derivative of e^{3x}-1-3x

\frac{d}{d x} (e^{3 x} - 1 - 3 x)

derivative of f(x)=(2(-x^2+1))/((x^2+1))derivative of

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

Frequently Asked Questions (FAQ)

What is the derivative of (x^2/(7+x)) ?
The derivative of (x^2/(7+x)) is (14x+x^2)/((7+x)^2)
What is the first derivative of (x^2/(7+x)) ?
The first derivative of (x^2/(7+x)) is (14x+x^2)/((7+x)^2)