What is the derivative of 1/((3x+4)^3) ?

The derivative of 1/((3x+4)^3) is -9/((3x+4)^4)

What is the first derivative of 1/((3x+4)^3) ?

The first derivative of 1/((3x+4)^3) is -9/((3x+4)^4)

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derivative of

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

- \frac{9}{( 3 x + 4 ) ^{4}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x + 4) = 3

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

Simplify

- \frac{3}{( 3 x + 4 ) ^{4}} \cdot 3 : - \frac{9}{( 3 x + 4 ) ^{4}}

= - \frac{9}{( 3 x + 4 ) ^{4}}

1 - 1 - x^{2}

f (x) = (3 x - 4) 2 (x - 2)

- t^{2} + 4 t + 4

\frac{d}{d x} ((i) \cdot (x^{- 5})^{5})

e^{2 x - y + z}

What is the derivative of 1/((3x+4)^3) ?
The derivative of 1/((3x+4)^3) is -9/((3x+4)^4)
What is the first derivative of 1/((3x+4)^3) ?
The first derivative of 1/((3x+4)^3) is -9/((3x+4)^4)