What is the derivative of x/(sqrt(x^2+49)) ?

The derivative of x/(sqrt(x^2+49)) is (49)/((x^2+49)sqrt(x^2+49))

What is the first derivative of x/(sqrt(x^2+49)) ?

The first derivative of x/(sqrt(x^2+49)) is (49)/((x^2+49)sqrt(x^2+49))

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\frac{d}{d x} (\frac{x}{x ^{2} + 49})

\frac{49}{( x ^{2} + 49 ) x ^{2} + 49}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} + 49})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} x ^{2} + 49 - \frac{d}{d x} ( x ^{2} + 49 ) x}{( x ^{2} + 49 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 49) = \frac{x}{x ^{2} + 49}

= \frac{1 \cdot x ^{2} + 49 - \frac{x}{x ^{2} + 49} x}{( x ^{2} + 49 ) ^{2}}

Simplify

\frac{1 \cdot x ^{2} + 49 - \frac{x}{x ^{2} + 49} x}{( x ^{2} + 49 ) ^{2}} : \frac{49}{( x ^{2} + 49 ) x ^{2} + 49}

= \frac{49}{( x ^{2} + 49 ) x ^{2} + 49}

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What is the derivative of x/(sqrt(x^2+49)) ?
The derivative of x/(sqrt(x^2+49)) is (49)/((x^2+49)sqrt(x^2+49))
What is the first derivative of x/(sqrt(x^2+49)) ?
The first derivative of x/(sqrt(x^2+49)) is (49)/((x^2+49)sqrt(x^2+49))