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Popular >

derivative of 1/(1+3x)

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

= \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

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

Simplify

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

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

Popular Examples

integral from 1 to e of ln(x^2)

\int_{1}^{e} ln (x^{2}) d x

integral from 110 to 160 of (160)/(3x^2)

\int_{110}^{160} \frac{160}{3 x ^{2}} d x

derivative of 3/(sqrt(x-2))

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

derivative of y=cos(a^3+x^3)derivative of

y = cos (a^{3} + x^{3})

(dy)/(dx)=-5e^{x+y}

\frac{d y}{d x} = - 5 e^{x + y}

Frequently Asked Questions (FAQ)

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