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Popular >

derivative of (2x+1/(3x-2))

Solution

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

Solution

- \frac{7}{( 3 x - 2 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 ( 3 x - 2 ) - 3 ( 2 x + 1 )}{( 3 x - 2 ) ^{2}} : - \frac{7}{( 3 x - 2 ) ^{2}}

= - \frac{7}{( 3 x - 2 ) ^{2}}

Popular Examples

limit as x approaches 3 of (x-3)/(x-2)

x \to 3 lim (\frac{x - 3}{x - 2})

tangent of y=7x-x^2,(1,6)tangent of

y = 7 x - x^{2}, (1, 6)

integral from 1 to 2 of x^4+2x^2

\int_{1}^{2} x^{4} + 2 x^{2} d x

integral from 0 to 1 of 5e^x-5xe^{x^2}

\int_{0}^{1} 5 e^{x} - 5 x e^{x^{2}} d x

integral of (16)/((x^2+4)^2)

\int \frac{16}{( x ^{2} + 4 ) ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of (2x+1/(3x-2)) ?
The derivative of (2x+1/(3x-2)) is -7/((3x-2)^2)
What is the first derivative of (2x+1/(3x-2)) ?
The first derivative of (2x+1/(3x-2)) is -7/((3x-2)^2)