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Popular >

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

Solution

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

Solution

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

Solution steps

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

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

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

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

Simplify

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

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

Popular Examples

integral of (2x^2)/(sqrt(1-6x^3))

\int \frac{2 x ^{2}}{1 - 6 x ^{3}} d x

integral of 1/(x*sqrt(9-x^2))

\int \frac{1}{x \cdot 9 - x ^{2}} d x

integral of 1/(xln^3(x))

\int \frac{1}{x ln ^{3} ( x )} d x

(\partial)/(\partial x)(tan(3x-5y))

\frac{\partial}{\partial x} (tan (3 x - 5 y))

(\partial)/(\partial x)(y^2-1)

\frac{\partial}{\partial x} (y^{2} - 1)

Frequently Asked Questions (FAQ)

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