What is the derivative of (3x^2/(sqrt(x))) ?

The derivative of (3x^2/(sqrt(x))) is (9sqrt(x))/2

What is the first derivative of (3x^2/(sqrt(x))) ?

The first derivative of (3x^2/(sqrt(x))) is (9sqrt(x))/2

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

\frac{9 x}{2}

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

3 \cdot \frac{3}{2} x^{\frac{3}{2} - 1} : \frac{9 x}{2}

= \frac{9 x}{2}

\frac{d}{d x} (- 0.4 x^{3})

x \to 0 lim (\frac{5}{4} π - π)

x \to 0 lim (\frac{1}{2 - e ^{\frac{1}{x}}})

t y^{^{'}} + y = t^{3}, y (1) = - 2

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

What is the derivative of (3x^2/(sqrt(x))) ?
The derivative of (3x^2/(sqrt(x))) is (9sqrt(x))/2
What is the first derivative of (3x^2/(sqrt(x))) ?
The first derivative of (3x^2/(sqrt(x))) is (9sqrt(x))/2