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

The derivative of 1/(3x+4) is -3/((3x+4)^2)

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

The first derivative of 1/(3x+4) is -3/((3x+4)^2)

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derivative of

\frac{1}{3 x + 4}

- \frac{3}{( 3 x + 4 ) ^{2}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{1}{( 3 x + 4 ) ^{2}} \frac{d}{d x} (3 x + 4)

= - \frac{1}{( 3 x + 4 ) ^{2}} \frac{d}{d x} (3 x + 4)

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

= - \frac{1}{( 3 x + 4 ) ^{2}} \cdot 3

Simplify

- \frac{1}{( 3 x + 4 ) ^{2}} \cdot 3 : - \frac{3}{( 3 x + 4 ) ^{2}}

= - \frac{3}{( 3 x + 4 ) ^{2}}

x \to 4 lim (- \frac{3 x}{7} + \frac{8}{7})

x \to 9 - lim (81 - x^{2})

\frac{d}{d x} ((x^{2} - 4)^{\frac{2}{3}})

sin (b x)

2 x - 1

What is the derivative of 1/(3x+4) ?
The derivative of 1/(3x+4) is -3/((3x+4)^2)
What is the first derivative of 1/(3x+4) ?
The first derivative of 1/(3x+4) is -3/((3x+4)^2)