What is the derivative of (3-1/x /(x+5)) ?

The derivative of (3-1/x /(x+5)) is (-3x^2+2x+5)/(x^2(x+5)^2)

What is the first derivative of (3-1/x /(x+5)) ?

The first derivative of (3-1/x /(x+5)) is (-3x^2+2x+5)/(x^2(x+5)^2)

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Popular >

\frac{d}{d x} (\frac{3 - \frac{1}{x}}{x + 5})

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

Solution steps

\frac{d}{d x} (\frac{3 - \frac{1}{x}}{x + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 - \frac{1}{x} ) ( x + 5 ) - \frac{d}{d x} ( x + 5 ) ( 3 - \frac{1}{x} )}{( x + 5 ) ^{2}}

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

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

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

Simplify

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

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

\int x^{2} - 2 x + 1 d x

\frac{d}{d x} (x \cdot e^{x^{2}})

\int \frac{cot ( x )}{sin ( x )} d x

csc (e^{2 x})

\frac{1}{p - p ^{2}} d p = d t

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