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Popular >

derivative of (x+1/x)^3

Solution

derivative of

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

Solution

3 x^{2} - \frac{3}{x ^{2}} - \frac{3}{x ^{4}} + 3

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches 2 of 5x^3-9x^2+7

x \to 2 lim (5 x^{3} - 9 x^{2} + 7)

integral of x^3*cos(x)

\int x^{3} \cdot cos (x) d x

xln(x)=y(1+sqrt(8+y^2))y^'(x),y(1)=1

x ln (x) = y (1 + 8 + y^{2}) y^{^{'}} (x), y (1) = 1

derivative of in(x^2+1)

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

(dy)/(dx)=y^2+1

\frac{d y}{d x} = y^{2} + 1

Frequently Asked Questions (FAQ)

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