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

The derivative of sin(x^{1/2}) is (cos(x^{1/2}))/(2x^{1/2)}

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

The first derivative of sin(x^{1/2}) is (cos(x^{1/2}))/(2x^{1/2)}

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derivative of

sin (x^{\frac{1}{2}})

\frac{cos ( x ^{\frac{1}{2}} )}{2 x ^{\frac{1}{2}}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

\frac{- x}{( x - 1 )}

\frac{d}{d x} (cos^{2} (y) - sin^{2} (x))

f (x) = (6 x^{2} + 7 x)^{4}

y = \frac{3 x \cdot 5 + 2}{x}

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