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Popular >

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

Solution

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

Solution

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

Solution steps

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

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

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

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

Simplify

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

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

Popular Examples

tangent of f(x)=sqrt(x^2+3x),(1,2)tangent of

f (x) = x^{2} + 3 x, (1, 2)

integral of (9-9x)/(1-sqrt(x))

\int \frac{9 - 9 x}{1 - x} d x

tangent of y=sqrt(x),\at x=4 tangent of

y = x, at x = 4

sum from n=0 to infinity} 1/(sqrt(n) of-1/(\sqrt{n+1))

n = 0 \sum \infty \frac{1}{n} - \frac{1}{n + 1}

y^{'''}+4y^{''}+4y^'=8x

y^{^{'''}} + 4 y^{^{''}} + 4 y^{^{'}} = 8 x

Frequently Asked Questions (FAQ)

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