What is the derivative of ((2x+1))/(x^2) ?

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

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

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

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derivative of

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

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

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}) = 2 x

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

Simplify

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

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

\int \frac{x ^{2} - 2}{x ^{2}} d x

x \to 1 lim (ln (x))

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

\frac{\partial}{\partial x} (x^{2} + y)

\frac{d y}{d x} + y = \frac{1}{1 + x ^{2}}

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