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Question

If y=tanx, then d2ydx2=

A
xdydx
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B
2xdydx
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C
2ydydx
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D
ydydx
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Solution

The correct option is D 2ydydx
Given y=tanx
dydx=sec2x.......(1)
d2ydx2=2secx.(secx.tanx)=2sec2xtanx .....(2)
substituting the value of sec2x from (1) in (2) we get,
d2ydx2=2(dydx)tanx
Also we have y=tanx, substituting we get
d2ydx2=2ydydx
Hence, the answer is 2ydydx.

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