What is the derivative of (-3/(sqrt(x^2+9))) ?

The derivative of (-3/(sqrt(x^2+9))) is (3x)/((x^2+9)^{3/2)}

What is the first derivative of (-3/(sqrt(x^2+9))) ?

The first derivative of (-3/(sqrt(x^2+9))) is (3x)/((x^2+9)^{3/2)}

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\frac{d}{d x} (\frac{- 3}{x ^{2} + 9})

\frac{3 x}{( x ^{2} + 9 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{- 3}{x ^{2} + 9})

Simplify

\frac{- 3}{x ^{2} + 9} : - \frac{3}{x ^{2} + 9}

= \frac{d}{d x} (- \frac{3}{x ^{2} + 9})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 3 \frac{d}{d x} (\frac{1}{x ^{2} + 9})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= - 3 \frac{d}{d x} ((x^{2} + 9)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( x ^{2} + 9 ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{2} + 9)

= - \frac{1}{2 ( x ^{2} + 9 ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{2} + 9)

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

= - 3 (- \frac{1}{2 ( x ^{2} + 9 ) ^{\frac{3}{2}}} \cdot 2 x)

Simplify

- 3 (- \frac{1}{2 ( x ^{2} + 9 ) ^{\frac{3}{2}}} \cdot 2 x) : \frac{3 x}{( x ^{2} + 9 ) ^{\frac{3}{2}}}

= \frac{3 x}{( x ^{2} + 9 ) ^{\frac{3}{2}}}

\int \frac{x ^{2}}{a - x ^{2}} d x

\frac{d}{d x} (csc (x) cot (x))

f (t) = 80 e^{- \frac{t}{10}} - 40 t

\frac{x}{x - 7}

\int (sin^{2} (x) cos (x)) d x

What is the derivative of (-3/(sqrt(x^2+9))) ?
The derivative of (-3/(sqrt(x^2+9))) is (3x)/((x^2+9)^{3/2)}
What is the first derivative of (-3/(sqrt(x^2+9))) ?
The first derivative of (-3/(sqrt(x^2+9))) is (3x)/((x^2+9)^{3/2)}