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Popular >

derivative of f(x)=(2x+1)/(x+2)

Solution

derivative of

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

Solution

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

Solution steps

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

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

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

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

Simplify

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

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

Popular Examples

derivative of (sqrt(x)/2)

\frac{d}{d x} (\frac{x}{2})

11x-6ysqrt(x^2+1)(dy)/(dx)=0,y(0)=9

11 x - 6 y x^{2} + 1 \frac{d y}{d x} = 0, y (0) = 9

derivative of y=(2/((2x-6) 3/2))derivative of

y = (\frac{2}{( 2 x - 6 ) \frac{3}{2}})

tangent of-sin(x/2)tangent of

- sin (\frac{x}{2})

limit as x approaches-1 of 10x(14x-3)

x \to - 1 lim (10 x (14 x - 3))

Frequently Asked Questions (FAQ)

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