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

The derivative of (2x/(sqrt(x))) is 1/(sqrt(x))

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

The first derivative of (2x/(sqrt(x))) is 1/(sqrt(x))

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

\frac{1}{x}

Solution steps

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

Simplify

\frac{2 x}{x} : 2 x

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

Take the constant out:

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

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

Apply radical rule:

a = a^{\frac{1}{2}}

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

Apply the Power Rule:

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

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

Simplify

2 \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{1}{x}

= \frac{1}{x}

x \to 0 + lim (\frac{3}{x})

\int x^{27} e^{x^{28}} d x

\int cos^{4} (7 x + 8) d x

\int ln (10 x) d x

y^{^{'}} - \frac{4}{x} y = \frac{y ^{3}}{x ^{4}}

What is the derivative of (2x/(sqrt(x))) ?
The derivative of (2x/(sqrt(x))) is 1/(sqrt(x))
What is the first derivative of (2x/(sqrt(x))) ?
The first derivative of (2x/(sqrt(x))) is 1/(sqrt(x))