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Popular >

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

Solution

derivative of

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

Solution

- \frac{1}{x ^{2}}

Solution steps

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

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

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

\frac{d x}{d x} = 1

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

Simplify

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

= - \frac{1}{x ^{2}}

Popular Examples

\frac{d}{d t} (- 6 t)

inverse oflaplace (2x)/(x^2+2x)+x+5 inverse laplace

\frac{2 x}{x ^{2} + 2 x} + x + 5

limit as x approaches 1 of x^{1/(x-1)}

x \to 1 lim (x^{\frac{1}{x - 1}})

derivative of 1/((1+x))

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

derivative of (1+2x)e^{3x^2}derivative of

(1 + 2 x) e^{3 x^{2}}

Frequently Asked Questions (FAQ)

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