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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (\frac{1}{2}) = 0

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

= 0 - (- \frac{1}{4 x ^{\frac{3}{2}}})

Simplify

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

Popular Examples

limit as x approaches 0-of 2x-8x^2

x \to 0 - lim (2 x - 8 x^{2})

y^{''}-2y+y=(e^x)/(1+x^2)

y^{^{''}} - 2 y + y = \frac{e ^{x}}{1 + x ^{2}}

limit as x approaches 1+of sqrt(3x-3)+2

x \to 1 + lim (3 x - 3 + 2)

y^'sin(x)+ycos(x)=0,y(pi/4)=1

y^{^{'}} sin (x) + y cos (x) = 0, y (\frac{π}{4}) = 1

derivative of x^4tan(x)

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

Frequently Asked Questions (FAQ)

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