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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (4 u (x, y))

\frac{1}{3 x ^{2}}

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

\frac{d}{d x} (\frac{1}{2} x^{2} 36 - x^{2})

n = 0 \sum \infty 2^{n} 1^{n}

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