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Popular >

derivative of (2x^{3/2}/x)

Solution

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

Solution

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

Solution steps

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

Simplify

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

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Power Rule:

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

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

Simplify

2 \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{1}{x ^{\frac{1}{2}}}

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

Popular Examples

sum from n=1 to infinity of (3^n)/(n^3)

n = 1 \sum \infty \frac{3 ^{n}}{n ^{3}}

integral of (sin(2x))/((1+cos(2x))^3)

\int \frac{sin ( 2 x )}{( 1 + cos ( 2 x ) ) ^{3}} d x

derivative of f(x)=(x^5)/5+1/(12x^3)derivative of

f (x) = \frac{x ^{5}}{5} + \frac{1}{12 x ^{3}}

tangent of y=sin(2x)+sin(2)(2x)tangent of

y = sin (2 x) + sin (2) (2 x)

limit as x approaches-pi/2 of 2tan(x)

x \to - \frac{π}{2} lim (2 tan (x))

Frequently Asked Questions (FAQ)

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