if-y-sin-1-x-2-cos-1-x-2-find-dy-dx-

Question Number 28305 by NECx last updated on 23/Jan/18

i f y = \sin^{- 1} x^{2} + \cos^{- 1} x^{2}

f i n d d y / d x

Commented by abdo imad last updated on 23/Jan/18

y (x) = a r c s i n (x^{2}) + a r c o s (x^{2})

y^{^{'}} (x) = \frac{2 x}{\sqrt{1 - x^{4}}} + \frac{- 2 x}{\sqrt{1 - x^{4}}} = 0 \Rightarrow y (x) = λ \forall x \in R

y (0) = \frac{π}{2} \Rightarrow y (x) = \frac{π}{2} .

Commented by abdo imad last updated on 23/Jan/18

i f y o u m e a n y (x) = {(a r c s i n x)}^{2} + {(a r c o s x)}^{2}

y^{^{'}} (x) = 2 \frac{a r c s i n x}{\sqrt{1 - x^{2}}} - 2 \frac{a r c o s x}{\sqrt{1 - x^{2}}} = \frac{2}{\sqrt{1 - x^{2}}} (a r c s i n x - a r c o s x)

= \frac{- 2}{\sqrt{1 - x^{2}}} (a r c o s (- x) + a r c s i n (- x)) = \frac{- 2}{\sqrt{1 - x^{2}}} \frac{ξ π}{2}

= \frac{- π ξ}{\sqrt{1 - x^{2}}} w i t h ξ^{2} = 1 a n d - 1 < x < 1 .

Commented by NECx last updated on 24/Jan/18

t h a n k y o u s o m u c h .

Facebook Tweet Pin