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Popular >

derivative of (x+2/(3x-4))

Solution

\frac{d}{d x} (\frac{x + 2}{3 x - 4})

Solution

- \frac{10}{( 3 x - 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x + 2}{3 x - 4})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 2 ) ( 3 x - 4 ) - \frac{d}{d x} ( 3 x - 4 ) ( x + 2 )}{( 3 x - 4 ) ^{2}}

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

\frac{d}{d x} (3 x - 4) = 3

= \frac{1 \cdot ( 3 x - 4 ) - 3 ( x + 2 )}{( 3 x - 4 ) ^{2}}

Simplify

\frac{1 \cdot ( 3 x - 4 ) - 3 ( x + 2 )}{( 3 x - 4 ) ^{2}} : - \frac{10}{( 3 x - 4 ) ^{2}}

= - \frac{10}{( 3 x - 4 ) ^{2}}

Popular Examples

sum from n=1 to infinity of 8*(1/5)^n

n = 1 \sum \infty 8 \cdot (\frac{1}{5})^{n}

integral of (7x+1)/(x(x^2-1))

\int \frac{7 x + 1}{x ( x ^{2} - 1 )} d x

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\int_{0}^{3} \frac{1}{1 + x} d x

integral of (z^2)/(1^3)+z^3

\int \frac{z ^{2}}{1 ^{3}} + z^{3}

integral of 20x^3-12x^2+6x

\int 20 x^{3} - 12 x^{2} + 6 x d x

Frequently Asked Questions (FAQ)

What is the derivative of (x+2/(3x-4)) ?
The derivative of (x+2/(3x-4)) is -(10)/((3x-4)^2)
What is the first derivative of (x+2/(3x-4)) ?
The first derivative of (x+2/(3x-4)) is -(10)/((3x-4)^2)