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Popular >

derivative of (2x+1/(x+5))

Solution

\frac{d}{d x} (\frac{2 x + 1}{x + 5})

Solution

\frac{9}{( x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x + 1}{x + 5})

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 + 5 ) - \frac{d}{d x} ( x + 5 ) ( 2 x + 1 )}{( x + 5 ) ^{2}}

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

\frac{d}{d x} (x + 5) = 1

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

Simplify

\frac{2 ( x + 5 ) - 1 \cdot ( 2 x + 1 )}{( x + 5 ) ^{2}} : \frac{9}{( x + 5 ) ^{2}}

= \frac{9}{( x + 5 ) ^{2}}

Popular Examples

integral of (7/x-6/(x^3))

\int (\frac{7}{x} - \frac{6}{x ^{3}}) d x

limit as (x,y) approaches (1,-1) of (e^{-xy})(cos(x+y))

(x, y) \to (1, - 1) lim ((e^{- x y}) (cos (x + y)))

integral of+2x^2sec^2(x^3+1)

\int + 2 x^{2} sec^{2} (x^{3} + 1) d x

integral of xsqrt(1+2x)

\int x 1 + 2 x d x

integral from 0 to 3 of 1/(5x+1)

\int_{0}^{3} \frac{1}{5 x + 1} d x

Frequently Asked Questions (FAQ)

What is the derivative of (2x+1/(x+5)) ?
The derivative of (2x+1/(x+5)) is 9/((x+5)^2)
What is the first derivative of (2x+1/(x+5)) ?
The first derivative of (2x+1/(x+5)) is 9/((x+5)^2)