What is the derivative of 5x^{3/2} ?

The derivative of 5x^{3/2} is (15x^{1/2})/2

What is the first derivative of 5x^{3/2} ?

The first derivative of 5x^{3/2} is (15x^{1/2})/2

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derivative of

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

\frac{15 x ^{\frac{1}{2}}}{2}

Solution steps

\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 ^{\frac{1}{2}}}{2}

= \frac{15 x ^{\frac{1}{2}}}{2}

e^{\frac{x ^{2}}{2}}

x, x

f (x) = \frac{1}{- 2 + ( 3 x + 1 ) ^{2}}

\int (5 x^{2} + 1) 5 x^{3} + 3 x - 2 d x

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

What is the derivative of 5x^{3/2} ?
The derivative of 5x^{3/2} is (15x^{1/2})/2
What is the first derivative of 5x^{3/2} ?
The first derivative of 5x^{3/2} is (15x^{1/2})/2