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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Apply the Power Rule:

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

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

Simplify

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

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

(3.2) (1.6)

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

\int arccot (13 y) d y

\int 1 + cos (8 x) d x

\frac{d}{d x} (cos (arctan (5 x)))

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