What is the derivative of 5/((1+3x)) ?

The derivative of 5/((1+3x)) is -(15)/((1+3x)^2)

What is the first derivative of 5/((1+3x)) ?

The first derivative of 5/((1+3x)) is -(15)/((1+3x)^2)

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derivative of

\frac{5}{( 1 + 3 x )}

- \frac{15}{( 1 + 3 x ) ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

5 (- \frac{1}{( 1 + 3 x ) ^{2}} \cdot 3) : - \frac{15}{( 1 + 3 x ) ^{2}}

= - \frac{15}{( 1 + 3 x ) ^{2}}

\frac{d}{d t} (- 38 t + 220)

(x^{2} + 9) (x^{3} + 5)

\frac{( x ^{4} + 9 )}{x ^{2}}

tan^{- 2} (x)

2 t + 5

What is the derivative of 5/((1+3x)) ?
The derivative of 5/((1+3x)) is -(15)/((1+3x)^2)
What is the first derivative of 5/((1+3x)) ?
The first derivative of 5/((1+3x)) is -(15)/((1+3x)^2)