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Popular >

derivative of (cx^{1/2})

Solution

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

Solution

\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}}}

Popular Examples

integral of (x^3+64)/(x^2+64)

\int \frac{x ^{3} + 64}{x ^{2} + 64} d x

limit as t approaches 2-of-(3t)/(t-2)

t \to 2 - lim (- \frac{3 t}{t - 2})

limit as x approaches 1+of 3/(x^2-1)

x \to 1 + lim (\frac{3}{x ^{2} - 1})

derivative of 11x^2e^x derivative of

11 x^{2} e^{x}

tangent of 4x^2 tangent of

4 x^{2}

Frequently Asked Questions (FAQ)

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)}