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Popular >

derivative of ((x+1^3)/x)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

Popular Examples

y^{^{'}} = y^{2} - (x y)^{2}

integral of 1/(3sqrt(x)(2+\sqrt{x))}

\int \frac{1}{3 x ( 2 + x )} d x

limit as x approaches 2-of arcsin(x/2)

x \to 2 - lim (arcsin (\frac{x}{2}))

limit as x approaches-1 of (x+2x^4)^3

x \to - 1 lim ((x + 2 x^{4})^{3})

integral of y^x

\int y^{x} d x

Frequently Asked Questions (FAQ)

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