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Popular >

derivative of sqrt(x)-1/(sqrt(x))

Solution

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

Solution

\frac{1}{2 x} + \frac{1}{2 x ^{\frac{3}{2}}}

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

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

Simplify

= \frac{1}{2 x} + \frac{1}{2 x ^{\frac{3}{2}}}

Popular Examples

(dy)/(dx)=e^{4x-y}

\frac{d y}{d x} = e^{4 x - y}

derivative of-x^4

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

limit as h approaches 0 of ((-4+h)+4)/h

h \to 0 lim (\frac{( - 4 + h ) + 4}{h})

integral of (8x^2+5x+8)/((x^2+1)^2)

\int \frac{8 x ^{2} + 5 x + 8}{( x ^{2} + 1 ) ^{2}} d x

integral of 2sin(x)

\int 2 sin (x) d x

Frequently Asked Questions (FAQ)

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