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Question
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cosec x . cot x
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Solution
y = u v
⇒ y’ = uv’ + vu’
u = cosec x
⇒ u’ = – cosec x cot x
v = cot x
⇒ v’ = – cosec2 x
`("d"y)/("d"x)` = (cosec x)(– cosec2x) + cot x(– coseç x cot x)
= cosec3x – cosec x cot2x
= – cosec x (cosec2x + cot2x)
= `- 1/sinx (1/(sin^2x)+ (cos^2x)/(sin^2x))`
= `- ((1 + cos^2x))/(sinx sin^2x)`
= `- ((1 + cos^2x))/(sin^x)`
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