What is the derivative of (20x+x^2/((10+x)^2)) ?

The derivative of (20x+x^2/((10+x)^2)) is (200)/((10+x)^3)

What is the first derivative of (20x+x^2/((10+x)^2)) ?

The first derivative of (20x+x^2/((10+x)^2)) is (200)/((10+x)^3)

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\frac{d}{d x} (\frac{20 x + x ^{2}}{( 10 + x ) ^{2}})

\frac{200}{( 10 + x ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{20 x + x ^{2}}{( 10 + x ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 20 x + x ^{2} ) ( 10 + x ) ^{2} - \frac{d}{d x} ( ( 10 + x ) ^{2} ) ( 20 x + x ^{2} )}{( ( 10 + x ) ^{2} ) ^{2}}

\frac{d}{d x} (20 x + x^{2}) = 20 + 2 x

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

= \frac{( 20 + 2 x ) ( 10 + x ) ^{2} - 2 ( 10 + x ) ( 20 x + x ^{2} )}{( ( 10 + x ) ^{2} ) ^{2}}

Simplify

\frac{( 20 + 2 x ) ( 10 + x ) ^{2} - 2 ( 10 + x ) ( 20 x + x ^{2} )}{( ( 10 + x ) ^{2} ) ^{2}} : \frac{200}{( 10 + x ) ^{3}}

= \frac{200}{( 10 + x ) ^{3}}

What is the derivative of (20x+x^2/((10+x)^2)) ?
The derivative of (20x+x^2/((10+x)^2)) is (200)/((10+x)^3)
What is the first derivative of (20x+x^2/((10+x)^2)) ?
The first derivative of (20x+x^2/((10+x)^2)) is (200)/((10+x)^3)