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

The derivative of f(x)=((x^2))/((5+x)) is (10x+x^2)/((5+x)^2)

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

The first derivative of f(x)=((x^2))/((5+x)) is (10x+x^2)/((5+x)^2)

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derivative of

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

\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}}

f (x) = 4 x^{2} - 2 x + 6, at x = 4

\int_{0}^{1} 7 x 5^{x} d x

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

\int_{- 1}^{3} (x^{2} - 2 x - 3) d x

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

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