What is the derivative of y= x/(sqrt(x^2+5)) ?

The derivative of y= x/(sqrt(x^2+5)) is 5/((x^2+5)sqrt(x^2+5))

What is the first derivative of y= x/(sqrt(x^2+5)) ?

The first derivative of y= x/(sqrt(x^2+5)) is 5/((x^2+5)sqrt(x^2+5))

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derivative of

y = \frac{x}{x ^{2} + 5}

\frac{5}{( x ^{2} + 5 ) x ^{2} + 5}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} x ^{2} + 5 - \frac{d}{d x} ( x ^{2} + 5 ) x}{( x ^{2} + 5 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 5) = \frac{x}{x ^{2} + 5}

= \frac{1 \cdot x ^{2} + 5 - \frac{x}{x ^{2} + 5} x}{( x ^{2} + 5 ) ^{2}}

Simplify

\frac{1 \cdot x ^{2} + 5 - \frac{x}{x ^{2} + 5} x}{( x ^{2} + 5 ) ^{2}} : \frac{5}{( x ^{2} + 5 ) x ^{2} + 5}

= \frac{5}{( x ^{2} + 5 ) x ^{2} + 5}

What is the derivative of y= x/(sqrt(x^2+5)) ?
The derivative of y= x/(sqrt(x^2+5)) is 5/((x^2+5)sqrt(x^2+5))
What is the first derivative of y= x/(sqrt(x^2+5)) ?
The first derivative of y= x/(sqrt(x^2+5)) is 5/((x^2+5)sqrt(x^2+5))