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

Popular >

\frac{d}{d x} ((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}

\int_{2}^{\infty} 5 x^{- 2} d x

\int x 5 + 2 x^{2} d x

a^{2} d x = x x^{2} - a^{2} d y

e^{2 t} sin (3 t)

y = 3 x, y = 9, y = \frac{1}{4} x^{2}

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