What is the derivative of 5x^{0.5} ?

The derivative of 5x^{0.5} is (2.5)/(x^{0.5)}

What is the first derivative of 5x^{0.5} ?

The first derivative of 5x^{0.5} is (2.5)/(x^{0.5)}

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\frac{d}{d x} (5 x^{0.5})

\frac{2.5}{x ^{0.5}}

Solution steps

\frac{d}{d x} (5 x^{0.5})

Take the constant out:

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

= 5 \frac{d}{d x} (x^{0.5})

Apply the Power Rule:

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

= 5 \cdot 0.5 x^{0.5 - 1}

Simplify

5 \cdot 0.5 x^{0.5 - 1} : \frac{2.5}{x ^{0.5}}

= \frac{2.5}{x ^{0.5}}

6 x + 9

\int \frac{e ^{x} - 1}{e ^{x} + 1} d x

x \to 1 + lim (x^{2} + 1)

\int \frac{x}{x ^{3} - 1} d x

What is the derivative of 5x^{0.5} ?
The derivative of 5x^{0.5} is (2.5)/(x^{0.5)}
What is the first derivative of 5x^{0.5} ?
The first derivative of 5x^{0.5} is (2.5)/(x^{0.5)}