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Popular >

derivative of (x^3+7/x)

Solution

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

Solution

\frac{2 x ^{3} - 7}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

= \frac{3 x ^{2} x - 1 \cdot ( x ^{3} + 7 )}{x ^{2}}

Simplify

\frac{3 x ^{2} x - 1 \cdot ( x ^{3} + 7 )}{x ^{2}} : \frac{2 x ^{3} - 7}{x ^{2}}

= \frac{2 x ^{3} - 7}{x ^{2}}

Popular Examples

integral of sin^3(5x)cos^3(5x)

\int sin^{3} (5 x) cos^{3} (5 x) d x

derivative of (8+x^{1/x})

\frac{d}{d x} ((8 + x)^{\frac{1}{x}})

integral from 0 to 1 of (x^7)/(x^8-1)

\int_{0}^{1} \frac{x ^{7}}{x ^{8} - 1} d x

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

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

taylor tan(x), pi/4 taylor

tan (x), \frac{π}{4}

Frequently Asked Questions (FAQ)

What is the derivative of (x^3+7/x) ?
The derivative of (x^3+7/x) is (2x^3-7)/(x^2)
What is the first derivative of (x^3+7/x) ?
The first derivative of (x^3+7/x) is (2x^3-7)/(x^2)