Question

How do you find the derivative of (sin(x))^1/2? Would you use the power or chain rule?

Answer 1

power rule first and then chain rule.

Answer 2

Derivative of [ f(x) ]^n is: n * [ f(x) ]^(n-1) * f'(x)

Answer 3

try chain rule may b easier for you or which one do you find complex to use?

Answer 4

\[(\sin(x))^{1/2}\]
First the power rule.
\[\frac{ 1}{ 2 }(\sin(x))^{\frac{ 1 }{ 2 }-1}\]
Then the chain rule to take the derivative of the inside.
\[\frac{ 1}{ 2 }(\sin(x))^{-\frac{ 1 }{ 2 }}*\cos(x)\]
Last step is to simplify
\[\frac{ \cos(x) }{ 2\sqrt{\sin(x)} }\]