What is the derivative of (sqrt(x)dx) ?

The derivative of (sqrt(x)dx) is (3dsqrt(x))/2

What is the first derivative of (sqrt(x)dx) ?

The first derivative of (sqrt(x)dx) is (3dsqrt(x))/2

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

\frac{3 d x}{2}

Solution steps

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

Simplify

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

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

Treat

d

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

= d \frac{3}{2} x^{\frac{3}{2} - 1}

Simplify

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

= \frac{3 d x}{2}

\frac{d}{d x} (cos (\frac{1 - e ^{6 x}}{1 + e ^{6 x}}))

x \to \infty lim (9.9)

y^{^{'}} = \frac{x - y}{x + y}

\frac{d}{d x} (e^{2 x} 0.2)

x \to 0 lim (x cot (x))

What is the derivative of (sqrt(x)dx) ?
The derivative of (sqrt(x)dx) is (3dsqrt(x))/2
What is the first derivative of (sqrt(x)dx) ?
The first derivative of (sqrt(x)dx) is (3dsqrt(x))/2