What is the derivative of (432/((1+6x)^3)) ?

The derivative of (432/((1+6x)^3)) is -(7776)/((1+6x)^4)

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

The first derivative of (432/((1+6x)^3)) is -(7776)/((1+6x)^4)

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

- \frac{7776}{( 1 + 6 x ) ^{4}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{3}{( 1 + 6 x ) ^{4}} \frac{d}{d x} (1 + 6 x)

= - \frac{3}{( 1 + 6 x ) ^{4}} \frac{d}{d x} (1 + 6 x)

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

= 432 (- \frac{3}{( 1 + 6 x ) ^{4}} \cdot 6)

Simplify

432 (- \frac{3}{( 1 + 6 x ) ^{4}} \cdot 6) : - \frac{7776}{( 1 + 6 x ) ^{4}}

= - \frac{7776}{( 1 + 6 x ) ^{4}}

t a y l or e^{x}, x = 1

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What is the derivative of (432/((1+6x)^3)) ?
The derivative of (432/((1+6x)^3)) is -(7776)/((1+6x)^4)
What is the first derivative of (432/((1+6x)^3)) ?
The first derivative of (432/((1+6x)^3)) is -(7776)/((1+6x)^4)