What is the derivative of-(36/((1+6x)^2)) ?

The derivative of-(36/((1+6x)^2)) is (432)/((1+6x)^3)

What is the first derivative of-(36/((1+6x)^2)) ?

The first derivative of-(36/((1+6x)^2)) is (432)/((1+6x)^3)

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

\frac{432}{( 1 + 6 x ) ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{2}{( 1 + 6 x ) ^{3}} \frac{d}{d x} (1 + 6 x)

= - \frac{2}{( 1 + 6 x ) ^{3}} \frac{d}{d x} (1 + 6 x)

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

= - 36 (- \frac{2}{( 1 + 6 x ) ^{3}} \cdot 6)

Simplify

- 36 (- \frac{2}{( 1 + 6 x ) ^{3}} \cdot 6) : \frac{432}{( 1 + 6 x ) ^{3}}

= \frac{432}{( 1 + 6 x ) ^{3}}

\frac{d y}{d x} = \frac{9 x ^{2} - 6}{x ^{2}}

\frac{\partial}{\partial y} (x e^{y} - x^{5} + y - 3)

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

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

\int_{0}^{1} - 8 x 5^{x} d x

What is the derivative of-(36/((1+6x)^2)) ?
The derivative of-(36/((1+6x)^2)) is (432)/((1+6x)^3)
What is the first derivative of-(36/((1+6x)^2)) ?
The first derivative of-(36/((1+6x)^2)) is (432)/((1+6x)^3)