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Popular >

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

Solution

derivative of

y = \frac{3 x - 2}{2 x + 1}

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

3 (2 x + 1) - 2 (3 x - 2) : 7

= \frac{7}{( 2 x + 1 ) ^{2}}

Popular Examples

(\partial)/(\partial x)((2y)/((x+y)^2))

\frac{\partial}{\partial x} (\frac{2 y}{( x + y ) ^{2}})

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

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

area y=3sqrt(x),x+y=4,y=1 area

y = 3 x, x + y = 4, y = 1

integral from-1 to 1 of (5r)/((4+r^2)^2)

\int_{- 1}^{1} \frac{5 r}{( 4 + r ^{2} ) ^{2}} d r

(\partial)/(\partial x)(x/(x^2+xy+y^2))

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + x y + y ^{2}})

Frequently Asked Questions (FAQ)

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