If y -sin -sin x -cos x -F ind dy - dx

Putting (sin x+cos x)=t and √((sin x+cos x))=√(t) =u, we get y=sin u, u=√(t) and t=(sin x+cos x). ∴dy/du=cos u,du/dt=1/2t^ 1/2=1/2√(t) and dt/dx=(cos x sin x.) ...

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Byju's Answer

Standard XII

Mathematics

Functions

If y =sin √si...

Question

If $y = s i n (\sqrt{s i n x + c o s x}) . F i n d \frac{d y}{d x}$

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Solution

Putting $(s i n x + c o s x) = t a n d \sqrt{(s i n x + c o s x)} = \sqrt{t} = u, w e g e t$

$y = s i n u, u = \sqrt{t} a n d t = (s i n x + c o s x) .$

$∴ \frac{d y}{d u} = c o s u, \frac{d u}{d t} = \frac{1}{2} t^{- 1 / 2} = \frac{1}{2 \sqrt{t}}$

and $\frac{d t}{d x} = (c o s x - s i n x .)$

So, $\frac{d y}{d x} = (\frac{d y}{d u} \times \frac{d u}{d t} \times \frac{d t}{d x}) = \frac{c o s u}{2 \sqrt{t}} . (c o s x - s i n x)$

$= \frac{c o s \sqrt{t}}{2 \sqrt{t}} . (c o s x - s i n x) [∵ u = \sqrt{t}]$

$= \frac{c o s (\sqrt{s i n x + c o s x}) (c o s x - s i n x)}{2 \sqrt{s i n x + c o s x}} [∵ t = (s i n x + c o s x)]$

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If y=sin(√sin x+cos x).Find dydx

If $y = s i n (\sqrt{s i n x + c o s x}) . F i n d \frac{d y}{d x}$