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Popular >

derivative of x/(sqrt(x^2+6))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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