What is the derivative of (5x^2)/(sqrt(x)) ?

The derivative of (5x^2)/(sqrt(x)) is (15sqrt(x))/2

What is the first derivative of (5x^2)/(sqrt(x)) ?

The first derivative of (5x^2)/(sqrt(x)) is (15sqrt(x))/2

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derivative of

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

\frac{15 x}{2}

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

= \frac{15 x}{2}

What is the derivative of (5x^2)/(sqrt(x)) ?
The derivative of (5x^2)/(sqrt(x)) is (15sqrt(x))/2
What is the first derivative of (5x^2)/(sqrt(x)) ?
The first derivative of (5x^2)/(sqrt(x)) is (15sqrt(x))/2