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Popular >

derivative of (x^3-1/x)

Solution

\frac{d}{d x} (\frac{x ^{3} - 1}{x})

Solution

\frac{2 x ^{3} + 1}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{3} - 1}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{3} - 1 ) x - \frac{d x}{d x} ( x ^{3} - 1 )}{x ^{2}}

\frac{d}{d x} (x^{3} - 1) = 3 x^{2}

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

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

Simplify

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

= \frac{2 x ^{3} + 1}{x ^{2}}

Popular Examples

integral of 3x^7(x^8+1)^5

\int 3 x^{7} (x^{8} + 1)^{5} d x

area 2/x , 2/(x^2),1,6 area

\frac{2}{x}, \frac{2}{x ^{2}}, 1, 6

derivative of e^{-15x}

\frac{d}{d x} (e^{- 15 x})

integral from 1 to 27 of x^{1/3}

\int_{1}^{27} x^{\frac{1}{3}} d x

integral of-1/3 (x/3)^n

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

Frequently Asked Questions (FAQ)

What is the derivative of (x^3-1/x) ?
The derivative of (x^3-1/x) is (2x^3+1)/(x^2)
What is the first derivative of (x^3-1/x) ?
The first derivative of (x^3-1/x) is (2x^3+1)/(x^2)