What is the derivative of 1/(2+3x) ?

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

What is the first derivative of 1/(2+3x) ?

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 + 3 x) = 3

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

Simplify

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

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

\int csc (θ) d θ

x \to + 3 lim (6)

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\int_{0}^{\frac{π}{3}} 2 + sin (3 x) d x

\int e^{- i w x} d x

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