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Popular >

derivative of y=(1+1/x)^2

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches 1 of [f(x)+5g(x)]

x \to 1 lim ([f (x) + 5 g (x)])

x+y(dy)/(dx)=x-y

x + y \frac{d y}{d x} = x - y

tangent of f(x)=x^3-x,(1,0)tangent of

f (x) = x^{3} - x, (1, 0)

sum from n=0 to infinity of 1/(n(n+8))

n = 0 \sum \infty \frac{1}{n ( n + 8 )}

inverse oflaplace 5/(s*(2*s+1))inverse laplace

\frac{5}{s \cdot ( 2 \cdot s + 1 )}

Frequently Asked Questions (FAQ)

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