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Popular >

derivative of (x^3+2/x)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

derivative of \sqrt[3]{10x+5}

derivative of y=ln(7x^2+3y^2)derivative of

y = ln (7 x^{2} + 3 y^{2})

2y^{''}+3y^'+y=t^2+3sin(t)

2 y^{^{''}} + 3 y^{^{'}} + y = t^{2} + 3 sin (t)

integral of ((3*ln(x)-5)^4)/x

\int \frac{( 3 \cdot ln ( x ) - 5 ) ^{4}}{x} d x

y^'=7e^{4x-5y},y(0)=0

y^{^{'}} = 7 e^{4 x - 5 y}, y (0) = 0

Frequently Asked Questions (FAQ)

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