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Popular >

derivative of f(x)=(2x+1)/(x+3)

Solution

derivative of

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

Solution

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

Solution steps

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

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

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

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

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

Simplify

\frac{2 ( x + 3 ) - 1 \cdot ( 2 x + 1 )}{( x + 3 ) ^{2}} : \frac{5}{( x + 3 ) ^{2}}

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

Graph

Popular Examples

derivative of 1/(2sqrt(r)+7^{6/7)}derivative of

\frac{1}{2 r + 7 ^{\frac{6}{7}}}

derivative of 3sin(1+cos(4x^2))

\frac{d}{d x} (3 sin (1 + cos (4) x^{2}))

integral from 0 to t of t^2e^{-t/3}

\int_{0}^{t} t^{2} e^{- \frac{t}{3}} d t

tangent of y= 5/x ,(5,1)tangent of

y = \frac{5}{x}, (5, 1)

integral from 1 to 8 of (sqrt(2/x))

\int_{1}^{8} (\frac{2}{x}) d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(2x+1)/(x+3) ?
The derivative of f(x)=(2x+1)/(x+3) is 5/((x+3)^2)
What is the first derivative of f(x)=(2x+1)/(x+3) ?
The first derivative of f(x)=(2x+1)/(x+3) is 5/((x+3)^2)