What is the derivative of (x^2)/(x+4) ?

The derivative of (x^2)/(x+4) is (x^2+8x)/((x+4)^2)

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

The first derivative of (x^2)/(x+4) is (x^2+8x)/((x+4)^2)

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derivative of

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

\frac{x ^{2} + 8 x}{( x + 4 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x + 4) = 1

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

Simplify

\frac{2 x ( x + 4 ) - 1 \cdot x ^{2}}{( x + 4 ) ^{2}} : \frac{x ^{2} + 8 x}{( x + 4 ) ^{2}}

= \frac{x ^{2} + 8 x}{( x + 4 ) ^{2}}

f (x) = 3 x^{2} - 2 x, at x = - 1

\frac{d}{d t} (0. 9^{t})

x \to 0 lim (\frac{x - 9}{x - 1})

\frac{d y}{d t} = \frac{1}{y}

n = 0 \sum \infty (- \frac{2}{3} x)^{n}

What is the derivative of (x^2)/(x+4) ?
The derivative of (x^2)/(x+4) is (x^2+8x)/((x+4)^2)
What is the first derivative of (x^2)/(x+4) ?
The first derivative of (x^2)/(x+4) is (x^2+8x)/((x+4)^2)