What is the derivative of x/(sqrt(x^2+8)) ?

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

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

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

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derivative of

\frac{x}{x ^{2} + 8}

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

\int_{- \infty}^{2} x e^{x} d x

s + 2

\frac{d}{d x} (6 x^{2} y - 3 x y^{2})

\int (5 x^{3}) d x

f (x) = - \frac{6}{( 3 x + 5 ) ^{2}}, at x = - 1

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