
Kevin J.
asked 10/23/23Use implicit differentiation to find the: write the solution of each number
9. y' of sec²x+csc²y = 9
ans. y'= tanx sec²x / coty csc²y
10. g(y)= cos y / 3 - 3 siny
1 Expert Answer

Doug C. answered 10/23/23
Math Tutor with Reputation to make difficult concepts understandable
For 9:
2[sec(x)][sec(x)tan(x)] + 2csc(y)[-csc(y)cot(y)]y' = 0
Divide by 2 and simplify:
sec2(x)tan(x) = csc2(y)cot(y)y'
Divide both sides by coefficient of y':
y ' = sec2(x)tan(x) / csc2(y)cot(y)
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Doug C.
Try to use grouping symbols when it is not clear what is intended. The problem: is it (1/3)cos(y) or is it cos(y/3)? Or it could even be: cos(y)/[3 - 3sin(y)]10/23/23