What is the derivative of (2x^2^{1/2}) ?

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

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

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

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

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

Solution steps

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

Simplify

(2 x^{2})^{\frac{1}{2}} : 2^{\frac{1}{2}} (x^{2})^{\frac{1}{2}}

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\int \frac{1}{x - 1} d x

x \to 2 lim (2 - x^{2})

\int_{1}^{e^{4}} x^{4} ln (x) d x

f (x) = x^{2} - 2 x + 5, at x = 1

8 + 5 x

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