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Popular >

derivative of (x^2+6/x)

Solution

\frac{d}{d x} (\frac{x ^{2} + 6}{x})

Solution

\frac{x ^{2} - 6}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 6}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{2} + 6 ) x - \frac{d x}{d x} ( x ^{2} + 6 )}{x ^{2}}

\frac{d}{d x} (x^{2} + 6) = 2 x

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

= \frac{2 xx - 1 \cdot ( x ^{2} + 6 )}{x ^{2}}

Simplify

\frac{2 xx - 1 \cdot ( x ^{2} + 6 )}{x ^{2}} : \frac{x ^{2} - 6}{x ^{2}}

= \frac{x ^{2} - 6}{x ^{2}}

Graph

Popular Examples

derivative of (x^2+4x/((3x^3+2)^4))

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

y^{^{'}} = (4 + 3 x)^{4}

integral of (x+9)ln(x)

\int (x + 9) ln (x) d x

taylor 1/(x^2+1),0 taylor

\frac{1}{x ^{2} + 1}, 0

derivative of (x^7/7+(2x)/3)

\frac{d}{d x} (\frac{x ^{7}}{7} + \frac{2 x}{3})

Frequently Asked Questions (FAQ)

What is the derivative of (x^2+6/x) ?
The derivative of (x^2+6/x) is (x^2-6)/(x^2)
What is the first derivative of (x^2+6/x) ?
The first derivative of (x^2+6/x) is (x^2-6)/(x^2)