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Popular >

derivative of (sqrt(x)+1/(sqrt(x))^2)

Solution

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

Solution

- \frac{1}{x ^{2}} + 1

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (2) = 0

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

= 1 + 0 - \frac{1}{x ^{2}}

Simplify

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

Popular Examples

d/(dt)((cos(t))/(sqrt(1+t^2)))

\frac{d}{d t} (\frac{cos ( t )}{1 + t ^{2}})

integral of (x^5)/(sqrt(a-bx^3))

\int \frac{x ^{5}}{a - b x ^{3}} d x

derivative of (x^5/(4-x^4))

\frac{d}{d x} (\frac{x ^{5}}{4 - x ^{4}})

derivative of (5x^{9x})

\frac{d}{d x} ((5 x)^{9 x})

derivative of x^4+3x^2

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

Frequently Asked Questions (FAQ)

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