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Popular >

derivative of 2sqrt(x)-1/(2sqrt(x))

Solution

derivative of

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

Solution

\frac{1}{x} + \frac{1}{4 x ^{\frac{3}{2}}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (\frac{1}{2 x}) = - \frac{1}{4 x ^{\frac{3}{2}}}

= \frac{1}{x} - (- \frac{1}{4 x ^{\frac{3}{2}}})

Simplify

= \frac{1}{x} + \frac{1}{4 x ^{\frac{3}{2}}}

Popular Examples

derivative of y=arcsin(x^4)derivative of

y = arcsin (x^{4})

(\partial)/(\partial x)(1/((1+x)))

\frac{\partial}{\partial x} (\frac{1}{( 1 + x )})

derivative of (x^2-3x+1)sqrt(25-x^2)derivative of

(x^{2} - 3 x + 1) 25 - x^{2}

limit as x approaches 1 of 7e^{x-1}

x \to 1 lim (7 e^{x - 1})

integral of (2-2x)

\int (2 - 2 x) d x

Frequently Asked Questions (FAQ)

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