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Popular >

derivative of 3x^2sqrt(x)

Solution

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

Solution

\frac{15 x ^{\frac{3}{2}}}{2}

Solution steps

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

Simplify

3 x^{2} x : 3 x^{\frac{5}{2}}

= \frac{d}{d x} (3 x^{\frac{5}{2}})

Take the constant out:

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

= 3 \frac{d}{d x} (x^{\frac{5}{2}})

Apply the Power Rule:

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

= 3 \cdot \frac{5}{2} x^{\frac{5}{2} - 1}

Simplify

3 \cdot \frac{5}{2} x^{\frac{5}{2} - 1} : \frac{15 x ^{\frac{3}{2}}}{2}

= \frac{15 x ^{\frac{3}{2}}}{2}

Popular Examples

limit as x approaches 0 of 5/(cos(5x))

x \to 0 lim (\frac{5}{cos ( 5 x )})

(\partial)/(\partial x)(3xy-x^2y)

\frac{\partial}{\partial x} (3 x y - x^{2} y)

integral from 2 to 4 of (1/2 x^3-3x+2)

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

(\partial)/(\partial x)(cos(ln(x)))

\frac{\partial}{\partial x} (cos (ln (x)))

integral of 9xe^{-9x}

\int 9 x e^{- 9 x} d x

Frequently Asked Questions (FAQ)

What is the derivative of 3x^2sqrt(x) ?
The derivative of 3x^2sqrt(x) is (15x^{3/2})/2
What is the first derivative of 3x^2sqrt(x) ?
The first derivative of 3x^2sqrt(x) is (15x^{3/2})/2