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Popular >

derivative of (x^2/((5+x)))

Solution

\frac{d}{d x} (\frac{x ^{2}}{( 5 + x )})

Solution

\frac{10 x + x ^{2}}{( 5 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{( 5 + x )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( 5 + x ) - \frac{d}{d x} ( 5 + x ) x ^{2}}{( 5 + x ) ^{2}}

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

\frac{d}{d x} (5 + x) = 1

= \frac{2 x ( 5 + x ) - 1 \cdot x ^{2}}{( 5 + x ) ^{2}}

Simplify

\frac{2 x ( 5 + x ) - 1 \cdot x ^{2}}{( 5 + x ) ^{2}} : \frac{10 x + x ^{2}}{( 5 + x ) ^{2}}

= \frac{10 x + x ^{2}}{( 5 + x ) ^{2}}

Graph

Popular Examples

join arctan(x)-pi/4 join

arctan (x) - \frac{π}{4}

(\partial)/(\partial x)((x^2)/(1+y^2))

\frac{\partial}{\partial x} (\frac{x ^{2}}{1 + y ^{2}})

limit as x approaches 35 of (x^2)/5-7/x

x \to 35 lim (\frac{x ^{2}}{5} - \frac{7}{x})

derivative of-x^2-4x-2

\frac{d}{d x} (- x^{2} - 4 x - 2)

derivative of (x^2+1/x)

\frac{d}{d x} (\frac{x ^{2} + 1}{x})

Frequently Asked Questions (FAQ)

What is the derivative of (x^2/((5+x))) ?
The derivative of (x^2/((5+x))) is (10x+x^2)/((5+x)^2)
What is the first derivative of (x^2/((5+x))) ?
The first derivative of (x^2/((5+x))) is (10x+x^2)/((5+x)^2)