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Question

If S=exsinx, find d2Sdx2

A
2exsinx
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B
excosx2
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C
2excosx
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D
exsinx2
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Solution

The correct option is C 2excosx
Given, S=exsinx
So, d2Sdx2=d(dSdx)dx
Thus, we have
dSdx=d(exsinx)dx=exdsinxdx+sinxdexdx
excosx+exsinx=ex(sinx+cosx)
Now, d2Sdx2=d(ex(sinx+cosx))dx
exd(sinx+cosx)dx+(sinx+cosx)dexdx
ex(cosxsinx)+ex(sinx+cosx)
ex(cosxsinx+sinx+cosx)=2excosx

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