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Popular >

derivative of y=(2x-3)/(4x+1)

Solution

derivative of

y = \frac{2 x - 3}{4 x + 1}

Solution

\frac{14}{( 4 x + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x - 3}{4 x + 1})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (4 x + 1) = 4

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

Expand

2 (4 x + 1) - 4 (2 x - 3) : 14

= \frac{14}{( 4 x + 1 ) ^{2}}

Popular Examples

(\partial)/(\partial x)(3(x-y)*e^{3y+2x^2})

\frac{\partial}{\partial x} (3 (x - y) \cdot e^{3 y + 2 x^{2}})

derivative of (sqrt(t))/(1+t^2)derivative of

\frac{t}{1 + t ^{2}}

integral of (x^4)/(4sqrt(x^2+1))

\int \frac{x ^{4}}{4 x ^{2} + 1} d x

integral from 1 to 2 of (x^2+3x^4)

\int_{1}^{2} (x^{2} + 3 x^{4}) d x

area x^2+1,x,[-1,2]area

x^{2} + 1, x, [- 1, 2]

Frequently Asked Questions (FAQ)

What is the derivative of y=(2x-3)/(4x+1) ?
The derivative of y=(2x-3)/(4x+1) is (14)/((4x+1)^2)
What is the first derivative of y=(2x-3)/(4x+1) ?
The first derivative of y=(2x-3)/(4x+1) is (14)/((4x+1)^2)