What is the derivative of f(x)=x^{0.5} ?

The derivative of f(x)=x^{0.5} is (0.5)/(x^{0.5)}

What is the first derivative of f(x)=x^{0.5} ?

The first derivative of f(x)=x^{0.5} is (0.5)/(x^{0.5)}

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derivative of

f (x) = x^{0.5}

\frac{0.5}{x ^{0.5}}

Solution steps

\frac{d}{d x} (x^{0.5})

Apply the Power Rule:

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

= 0.5 x^{0.5 - 1}

Simplify

0.5 x^{0.5 - 1} : \frac{0.5}{x ^{0.5}}

= \frac{0.5}{x ^{0.5}}

What is the derivative of f(x)=x^{0.5} ?
The derivative of f(x)=x^{0.5} is (0.5)/(x^{0.5)}
What is the first derivative of f(x)=x^{0.5} ?
The first derivative of f(x)=x^{0.5} is (0.5)/(x^{0.5)}