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Popular Calculus >

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

Solution

derivative of

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

Solution

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

Solution steps

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

\frac{d}{d x} (2 x^{2} + 1) = 4 x

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

= \frac{4 xx - 1 \cdot ( 2 x ^{2} + 1 )}{x ^{2}}

Simplify

\frac{4 xx - 1 \cdot ( 2 x ^{2} + 1 )}{x ^{2}} : \frac{2 x ^{2} - 1}{x ^{2}}

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

Graph

Popular Examples

derivative of (sqrt(25-x^2)/(32x))

\frac{d}{d x} (\frac{25 - x ^{2}}{32 x})

integral from-1 to 1 of x^2e^{x^3+1}

\int_{- 1}^{1} x^{2} e^{x^{3} + 1} d x

derivative of \sqrt[4]{x^5}-3/(x^2)

\frac{d}{d x} (4 x^{5} - \frac{3}{x ^{2}})

derivative of e^{4x^2}*8x

\frac{d}{d x} (e^{4 x^{2}} \cdot 8 x)

derivative of f(x)=x^3-15x

d er i v a t i v e f (x) = x^{3} - 15 x

Frequently Asked Questions (FAQ)

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