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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

3 (\frac{x + 1}{x})^{2} (- \frac{1}{x ^{2}}) : - \frac{3 ( x + 1 ) ^{2}}{x ^{4}}

= - \frac{3 ( x + 1 ) ^{2}}{x ^{4}}

Popular Examples

derivative of (x^2/(x^2-16))

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} - 16})

integral of x^9ln(x)

\int x^{9} ln (x) d x

tangent of f(x)=(13x-1)^{-1/3},\at x=5 tangent of

f (x) = (13 x - 1)^{- \frac{1}{3}}, at x = 5

derivative of t/((t-9)^2)derivative of

\frac{t}{( t - 9 ) ^{2}}

25y^{''}+30y^'+9y=0

25 y^{^{''}} + 30 y^{^{'}} + 9 y = 0

Frequently Asked Questions (FAQ)

What is the derivative of ((x+1/x)^3) ?
The derivative of ((x+1/x)^3) is -(3(x+1)^2)/(x^4)
What is the first derivative of ((x+1/x)^3) ?
The first derivative of ((x+1/x)^3) is -(3(x+1)^2)/(x^4)