What is the derivative of x/(sqrt(x^2+7)) ?

The derivative of x/(sqrt(x^2+7)) is 7/((x^2+7)sqrt(x^2+7))

What is the first derivative of x/(sqrt(x^2+7)) ?

The first derivative of x/(sqrt(x^2+7)) is 7/((x^2+7)sqrt(x^2+7))

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\frac{d}{d x} (\frac{x}{x ^{2} + 7})

\frac{7}{( x ^{2} + 7 ) x ^{2} + 7}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} + 7})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} x ^{2} + 7 - \frac{d}{d x} ( x ^{2} + 7 ) x}{( x ^{2} + 7 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 7) = \frac{x}{x ^{2} + 7}

= \frac{1 \cdot x ^{2} + 7 - \frac{x}{x ^{2} + 7} x}{( x ^{2} + 7 ) ^{2}}

Simplify

\frac{1 \cdot x ^{2} + 7 - \frac{x}{x ^{2} + 7} x}{( x ^{2} + 7 ) ^{2}} : \frac{7}{( x ^{2} + 7 ) x ^{2} + 7}

= \frac{7}{( x ^{2} + 7 ) x ^{2} + 7}

x \to 0 lim (7 cot^{4} (3 x))

\int \frac{cos ( x )}{x} d x

f (x) = 5 (7 + x)

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

x \to 1 - lim (x)

What is the derivative of x/(sqrt(x^2+7)) ?
The derivative of x/(sqrt(x^2+7)) is 7/((x^2+7)sqrt(x^2+7))
What is the first derivative of x/(sqrt(x^2+7)) ?
The first derivative of x/(sqrt(x^2+7)) is 7/((x^2+7)sqrt(x^2+7))