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Popular >

derivative of y=(x+x^{-1})^3

Solution

derivative of

y = (x + x^{- 1})^{3}

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

3 (x + x^{- 1})^{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

derivative of (x+2^{1/2})

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

(\partial)/(\partial x)(ln(x^2+y-5))

\frac{\partial}{\partial x} (ln (x^{2} + y - 5))

(dy)/(dx)+y=5sin(2x)

\frac{d y}{d x} + y = 5 sin (2 x)

derivative of 3(x-2^2)

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

tangent of y=2sqrt(x)-x+1,(4,1)tangent of

y = 2 x - x + 1, (4, 1)

Frequently Asked Questions (FAQ)

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