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Popular >

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

Solution

derivative of

\frac{2 x + 3}{3 x + 2}

Solution

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

Solution steps

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

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

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

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

Simplify

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

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

Popular Examples

integral from 0 to 1 of z/((z^2+1)^3)

\int_{0}^{1} \frac{z}{( z ^{2} + 1 ) ^{3}} d z

limit as x approaches 0+of ln(x^3)

x \to 0 + lim (ln (x^{3}))

(1+t^2)y^'+4ty=t

(1 + t^{2}) y^{^{'}} + 4 t y = t

limit as x approaches-4 of 1/((x+4)^4)

x \to - 4 lim (\frac{1}{( x + 4 ) ^{4}})

derivative of 10x+4y

\frac{d}{d x} (10 x + 4 y)

Frequently Asked Questions (FAQ)

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