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

The derivative of y=(x^2)/((x+2)) is (x^2+4x)/((x+2)^2)

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

The first derivative of y=(x^2)/((x+2)) is (x^2+4x)/((x+2)^2)

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derivative of

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

\frac{x ^{2} + 4 x}{( x + 2 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 x ( x + 2 ) - 1 \cdot x ^{2}}{( x + 2 ) ^{2}} : \frac{x ^{2} + 4 x}{( x + 2 ) ^{2}}

= \frac{x ^{2} + 4 x}{( x + 2 ) ^{2}}

ln (x^{8})

\int \frac{sin ^{2} ( θ )}{cos ^{4} ( θ )} d θ

\frac{\partial}{\partial x} (- \frac{v ( x , t )}{b ( x , t ) ( x - v ( x , t ) t )})

\frac{d y}{y} = d x

\frac{1}{x}

What is the derivative of y=(x^2)/((x+2)) ?
The derivative of y=(x^2)/((x+2)) is (x^2+4x)/((x+2)^2)
What is the first derivative of y=(x^2)/((x+2)) ?
The first derivative of y=(x^2)/((x+2)) is (x^2+4x)/((x+2)^2)