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Question

If (sinx)(cosy)=12 then d2ydx2 at (π4,π4) is equal to

A
4
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B
2
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C
6
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D
0
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Solution

The correct option is A 4
Differentiating both sides, we have
cosxcosysinxsinydydx=0
Putting x=y=π4
We have dydx(π4,π4)=1

Differentiating again, we get
sinxcosycosxsiny(dydx)cosxsinydydx

sinxcosy(dydx)2sinxsinyd2ydx2=0

Putting x=y=π4

d2ydx2(π4,π4)=4

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