What is the derivative of 2/(3x+5) ?

The derivative of 2/(3x+5) is -6/((3x+5)^2)

What is the first derivative of 2/(3x+5) ?

The first derivative of 2/(3x+5) is -6/((3x+5)^2)

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derivative of

\frac{2}{3 x + 5}

- \frac{6}{( 3 x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2}{3 x + 5})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{1}{3 x + 5})

Apply exponent rule:

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

= 2 \frac{d}{d x} ((3 x + 5)^{- 1})

Apply the chain rule:

- \frac{1}{( 3 x + 5 ) ^{2}} \frac{d}{d x} (3 x + 5)

= - \frac{1}{( 3 x + 5 ) ^{2}} \frac{d}{d x} (3 x + 5)

\frac{d}{d x} (3 x + 5) = 3

= 2 (- \frac{1}{( 3 x + 5 ) ^{2}} \cdot 3)

Simplify

2 (- \frac{1}{( 3 x + 5 ) ^{2}} \cdot 3) : - \frac{6}{( 3 x + 5 ) ^{2}}

= - \frac{6}{( 3 x + 5 ) ^{2}}

\frac{d}{d x} (\frac{5 x}{x + 4})

\int_{- 4}^{4} (3 - ∣ x ∣) d x

y = (x^{2} + 4)^{\frac{2}{3}}, at x = 2

y = 5 ln (4 x^{2} + 1)

\int t e^{4 t} d t

What is the derivative of 2/(3x+5) ?
The derivative of 2/(3x+5) is -6/((3x+5)^2)
What is the first derivative of 2/(3x+5) ?
The first derivative of 2/(3x+5) is -6/((3x+5)^2)