What is the derivative of x/(sqrt(x^2+9)) ?

The derivative of x/(sqrt(x^2+9)) is 9/((x^2+9)sqrt(x^2+9))

What is the first derivative of x/(sqrt(x^2+9)) ?

The first derivative of x/(sqrt(x^2+9)) is 9/((x^2+9)sqrt(x^2+9))

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\frac{d}{d x} (\frac{x}{x ^{2} + 9})

\frac{9}{( x ^{2} + 9 ) x ^{2} + 9}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} + 9})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} x ^{2} + 9 - \frac{d}{d x} ( x ^{2} + 9 ) x}{( x ^{2} + 9 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 9) = \frac{x}{x ^{2} + 9}

= \frac{1 \cdot x ^{2} + 9 - \frac{x}{x ^{2} + 9} x}{( x ^{2} + 9 ) ^{2}}

Simplify

\frac{1 \cdot x ^{2} + 9 - \frac{x}{x ^{2} + 9} x}{( x ^{2} + 9 ) ^{2}} : \frac{9}{( x ^{2} + 9 ) x ^{2} + 9}

= \frac{9}{( x ^{2} + 9 ) x ^{2} + 9}

x \to 0 lim (\frac{∣ x ∣}{x ^{2} + x})

\int tan (6 x se) c^{2} 6 x d x

\frac{9 e ^{2 w} + e ^{w}}{e ^{w}}

\frac{d y}{d x} = x^{4} y^{- 3}

What is the derivative of x/(sqrt(x^2+9)) ?
The derivative of x/(sqrt(x^2+9)) is 9/((x^2+9)sqrt(x^2+9))
What is the first derivative of x/(sqrt(x^2+9)) ?
The first derivative of x/(sqrt(x^2+9)) is 9/((x^2+9)sqrt(x^2+9))