What is the derivative of (x^2)/(x+6) ?

The derivative of (x^2)/(x+6) is (x^2+12x)/((x+6)^2)

What is the first derivative of (x^2)/(x+6) ?

The first derivative of (x^2)/(x+6) is (x^2+12x)/((x+6)^2)

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derivative of

\frac{x ^{2}}{x + 6}

\frac{x ^{2} + 12 x}{( x + 6 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{x + 6})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( x + 6 ) - \frac{d}{d x} ( x + 6 ) x ^{2}}{( x + 6 ) ^{2}}

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

\frac{d}{d x} (x + 6) = 1

= \frac{2 x ( x + 6 ) - 1 \cdot x ^{2}}{( x + 6 ) ^{2}}

Simplify

\frac{2 x ( x + 6 ) - 1 \cdot x ^{2}}{( x + 6 ) ^{2}} : \frac{x ^{2} + 12 x}{( x + 6 ) ^{2}}

= \frac{x ^{2} + 12 x}{( x + 6 ) ^{2}}

\frac{d}{d x} (x^{2} e^{x} - e^{x})

x \to 6 lim (x π + x - 3)

\int 3 x^{2} (x^{3} + 4)^{10} d x

\frac{d}{d x} (\frac{5 x}{1 - x})

\frac{d}{d x} (2 x sin (2 x))

What is the derivative of (x^2)/(x+6) ?
The derivative of (x^2)/(x+6) is (x^2+12x)/((x+6)^2)
What is the first derivative of (x^2)/(x+6) ?
The first derivative of (x^2)/(x+6) is (x^2+12x)/((x+6)^2)