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Popular >

derivative of sqrt(x)-1/x

Solution

\frac{d}{d x} (x - \frac{1}{x})

Solution

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

Solution steps

\frac{d}{d x} (x - \frac{1}{x})

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

integral of (sqrt(2+x^2))/(sqrt(4-x^4))

\int \frac{2 + x ^{2}}{4 - x ^{4}} d x

integral of 49tan^5(x)sec^4(x)

\int 49 tan^{5} (x) sec^{4} (x) d x

limit as h approaches 0+of 2+h

h \to 0 + lim (2 + h)

(xdy)/(dx)=y^2-y

\frac{x d y}{d x} = y^{2} - y

derivative of x/(sqrt(x^2+9))

\frac{d}{d x} (\frac{x}{x ^{2} + 9})

Frequently Asked Questions (FAQ)

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