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

The derivative of (3x^2)(x^{1/2}) is (15x^{3/2})/2

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

The first derivative of (3x^2)(x^{1/2}) is (15x^{3/2})/2

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derivative of

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

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

Solution steps

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

Simplify

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

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x^{^{''}} + (x^{^{'}})^{2} = 0

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What is the derivative of (3x^2)(x^{1/2}) ?
The derivative of (3x^2)(x^{1/2}) is (15x^{3/2})/2
What is the first derivative of (3x^2)(x^{1/2}) ?
The first derivative of (3x^2)(x^{1/2}) is (15x^{3/2})/2