What is the derivative of arcsin({sqrt(((1-x)/2)})) ?

The derivative of arcsin({sqrt(((1-x)/2)})) is -1/(2sqrt(x+1)\sqrt{1-x)}

What is the first derivative of arcsin({sqrt(((1-x)/2)})) ?

The first derivative of arcsin({sqrt(((1-x)/2)})) is -1/(2sqrt(x+1)\sqrt{1-x)}

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\frac{d}{d x} (arcsin ({\frac{( 1 - x )}{2}}))

- \frac{1}{2 x + 1 1 - x}

Solution steps

\frac{d}{d x} (arcsin ((\frac{( 1 - x )}{2})))

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{1}{2 x + 1 1 - x}

s im pl i f y a^{2} (b + c) - (b + 3)^{3}

e x p an d (a + 8 y)^{3}

s im pl i f y (a^{2} \cdot b^{3})^{3} \cdot (a^{2} \cdot b)^{2}

s im pl i f y (x^{4})^{7}

f a c t or 8 s^{3} t^{3} + 64 s^{6} t^{6}

What is the derivative of arcsin({sqrt(((1-x)/2)})) ?
The derivative of arcsin({sqrt(((1-x)/2)})) is -1/(2sqrt(x+1)\sqrt{1-x)}
What is the first derivative of arcsin({sqrt(((1-x)/2)})) ?
The first derivative of arcsin({sqrt(((1-x)/2)})) is -1/(2sqrt(x+1)\sqrt{1-x)}