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Popular >

derivative of (1-3x/(1+3x))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

= - \frac{6}{( 1 + 3 x ) ^{2}}

Popular Examples

sum from n=1 to infinity of 1/(n^2)-1/n

n = 1 \sum \infty \frac{1}{n ^{2}} - \frac{1}{n}

sum from n=2 to infinity of n/(n+1)

n = 2 \sum \infty \frac{n}{n + 1}

limit as x approaches 5 of sqrt(x^2-25)

x \to 5 lim (x^{2} - 25)

integral of 2/((x^2-3x+2))

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

laplacetransform t^5e^{-6t}laplace transform

t^{5} e^{- 6 t}

Frequently Asked Questions (FAQ)

What is the derivative of (1-3x/(1+3x)) ?
The derivative of (1-3x/(1+3x)) is -6/((1+3x)^2)
What is the first derivative of (1-3x/(1+3x)) ?
The first derivative of (1-3x/(1+3x)) is -6/((1+3x)^2)