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Question

If y=sinmx then the value of the determinant ∣ ∣yy1y2y3y4y5y6y7y8∣ ∣, where yn=dnydxn, is

A
m9
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B
m2
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C
m3
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D
None of the above
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Solution

The correct option is D None of the above
We have y=sinmx,
y1=mcosmx,
y2=m2sinmx,
...
yn=mnsin(nπ2+mx)

=∣ ∣yy1y2y3y4y5y6y7y8∣ ∣

=∣ ∣ ∣sinmxmcosmxm2sinmxm3cosmxm4sinmxm5cosmxm6sinmxm7cosmxm8sinmx∣ ∣ ∣

=m12∣ ∣sinmxcosmxsinmxcosmxsinmxcosmxsinmxcosmxsinmx∣ ∣

R1R1+R3

=m12∣ ∣000cosmxsinmxcosmxsinmxcosmxsinmx∣ ∣

=0

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