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

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

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

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

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derivative of

y = (1 + sin (x))^{\frac{1}{2}}

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (1 + sin (x)) = cos (x)

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

Simplify

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

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

3 x^{4} + 1

arctan (\frac{1}{2 x - 1})

\frac{x}{( x ^{2} - 1 ) ^{4}}

6 x^{2} y^{2}

- 4 x^{2} cos (x)

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