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Popular >

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

Solution

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

Solution

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

Solution steps

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

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

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

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

Expand

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

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

Popular Examples

derivative of f(x)=(x^4)/3-6x derivative of

f (x) = \frac{x ^{4}}{3} - 6 x

limit as x approaches 0 of x^2+11

x \to 0 lim (x^{2} + 11)

tangent of f(x)=9x^2+94,\at x=6 tangent of

f (x) = 9 x^{2} + 94, at x = 6

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

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

(\partial)/(\partial x)(3/x-1-y)

\frac{\partial}{\partial x} (\frac{3}{x} - 1 - y)

Frequently Asked Questions (FAQ)

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