What is the derivative of x/(sqrt(x^2+81)) ?

The derivative of x/(sqrt(x^2+81)) is (81)/((x^2+81)sqrt(x^2+81))

What is the first derivative of x/(sqrt(x^2+81)) ?

The first derivative of x/(sqrt(x^2+81)) is (81)/((x^2+81)sqrt(x^2+81))

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\frac{d}{d x} (\frac{x}{x ^{2} + 81})

\frac{81}{( x ^{2} + 81 ) x ^{2} + 81}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} + 81})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} x ^{2} + 81 - \frac{d}{d x} ( x ^{2} + 81 ) x}{( x ^{2} + 81 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 81) = \frac{x}{x ^{2} + 81}

= \frac{1 \cdot x ^{2} + 81 - \frac{x}{x ^{2} + 81} x}{( x ^{2} + 81 ) ^{2}}

Simplify

\frac{1 \cdot x ^{2} + 81 - \frac{x}{x ^{2} + 81} x}{( x ^{2} + 81 ) ^{2}} : \frac{81}{( x ^{2} + 81 ) x ^{2} + 81}

= \frac{81}{( x ^{2} + 81 ) x ^{2} + 81}

What is the derivative of x/(sqrt(x^2+81)) ?
The derivative of x/(sqrt(x^2+81)) is (81)/((x^2+81)sqrt(x^2+81))
What is the first derivative of x/(sqrt(x^2+81)) ?
The first derivative of x/(sqrt(x^2+81)) is (81)/((x^2+81)sqrt(x^2+81))