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Popular >

derivative of 3/2 x^{1/2}

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

= \frac{3}{2} \cdot \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

\frac{3}{2} \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{3}{4 x ^{\frac{1}{2}}}

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

Popular Examples

integral of e^{5x}sin(4x)

\int e^{5 x} sin (4 x) d x

derivative of (5x^2-3(x^2+x+4))

\frac{d}{d x} ((5 x^{2} - 3) (x^{2} + x + 4))

(\partial)/(\partial y)(x+5y)

\frac{\partial}{\partial y} (x + 5 y)

derivative of 1/((3x^3+5x+7^{3/4)})

\frac{d}{d x} (\frac{1}{( 3 x ^{3} + 5 x + 7 ) ^{\frac{3}{4}}})

(e^y+6*x)*dx+(x*e^y)*dy=0

(e^{y} + 6 \cdot x) \cdot d x + (x \cdot e^{y}) \cdot d y = 0

Frequently Asked Questions (FAQ)

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