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

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

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

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

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derivative of

\frac{x ^{2}}{x + 10}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x + 10) = 1

= \frac{2 x ( x + 10 ) - 1 \cdot x ^{2}}{( x + 10 ) ^{2}}

Simplify

\frac{2 x ( x + 10 ) - 1 \cdot x ^{2}}{( x + 10 ) ^{2}} : \frac{x ^{2} + 20 x}{( x + 10 ) ^{2}}

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

e^{x} \frac{d x}{d t} = 3 t^{2}

\frac{( 3 x ^{2} - 6 ) ( x ^{2} - 2 )}{x ^{2} + 4}

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

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

x \to \infty lim (g (x))

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