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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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