What is the derivative of 6/(x^2+36) ?

The derivative of 6/(x^2+36) is -(12x)/((x^2+36)^2)

What is the first derivative of 6/(x^2+36) ?

The first derivative of 6/(x^2+36) is -(12x)/((x^2+36)^2)

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\frac{d}{d x} (\frac{6}{x ^{2} + 36})

- \frac{12 x}{( x ^{2} + 36 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{6}{x ^{2} + 36})

Take the constant out:

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

= 6 \frac{d}{d x} (\frac{1}{x ^{2} + 36})

Apply exponent rule:

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

= 6 \frac{d}{d x} ((x^{2} + 36)^{- 1})

Apply the chain rule:

- \frac{1}{( x ^{2} + 36 ) ^{2}} \frac{d}{d x} (x^{2} + 36)

= - \frac{1}{( x ^{2} + 36 ) ^{2}} \frac{d}{d x} (x^{2} + 36)

\frac{d}{d x} (x^{2} + 36) = 2 x

= 6 (- \frac{1}{( x ^{2} + 36 ) ^{2}} \cdot 2 x)

Simplify

6 (- \frac{1}{( x ^{2} + 36 ) ^{2}} \cdot 2 x) : - \frac{12 x}{( x ^{2} + 36 ) ^{2}}

= - \frac{12 x}{( x ^{2} + 36 ) ^{2}}

\int sin^{3} (x) cos^{3} (x) d x

(- 6, - 20), (1, 8)

f (x) = \frac{1}{x ln ( x )}

\int_{0}^{x} a^{2} - t^{2} d t

What is the derivative of 6/(x^2+36) ?
The derivative of 6/(x^2+36) is -(12x)/((x^2+36)^2)
What is the first derivative of 6/(x^2+36) ?
The first derivative of 6/(x^2+36) is -(12x)/((x^2+36)^2)