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

The derivative of (9x^2/(sqrt(x))) is (27sqrt(x))/2

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

The first derivative of (9x^2/(sqrt(x))) is (27sqrt(x))/2

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\frac{d}{d x} (\frac{9 x ^{2}}{x})

\frac{27 x}{2}

Solution steps

\frac{d}{d x} (\frac{9 x ^{2}}{x})

Simplify

\frac{9 x ^{2}}{x} : 9 x^{\frac{3}{2}}

= \frac{d}{d x} (9 x^{\frac{3}{2}})

Take the constant out:

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

= 9 \frac{d}{d x} (x^{\frac{3}{2}})

Apply the Power Rule:

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

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

Simplify

9 \cdot \frac{3}{2} x^{\frac{3}{2} - 1} : \frac{27 x}{2}

= \frac{27 x}{2}

\frac{d y}{d x} - \frac{y}{x} = 5 x e^{x}

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What is the derivative of (9x^2/(sqrt(x))) ?
The derivative of (9x^2/(sqrt(x))) is (27sqrt(x))/2
What is the first derivative of (9x^2/(sqrt(x))) ?
The first derivative of (9x^2/(sqrt(x))) is (27sqrt(x))/2