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

The derivative of (10x+x^2/((5+x)^2)) is (50)/((5+x)^3)

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

The first derivative of (10x+x^2/((5+x)^2)) is (50)/((5+x)^3)

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

\frac{50}{( 5 + x ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( 10 + 2 x ) ( 5 + x ) ^{2} - 2 ( 5 + x ) ( 10 x + x ^{2} )}{( ( 5 + x ) ^{2} ) ^{2}} : \frac{50}{( 5 + x ) ^{3}}

= \frac{50}{( 5 + x ) ^{3}}

\int r^{3} e^{- 2 r} d r

\frac{\partial}{\partial x} ((\frac{x}{y})^{z})

\int_{1}^{2} \frac{9 ln ( x )}{x ^{2}} d x

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

\frac{d}{d y} (e^{\frac{y}{x}})

What is the derivative of (10x+x^2/((5+x)^2)) ?
The derivative of (10x+x^2/((5+x)^2)) is (50)/((5+x)^3)
What is the first derivative of (10x+x^2/((5+x)^2)) ?
The first derivative of (10x+x^2/((5+x)^2)) is (50)/((5+x)^3)