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Home Q & A Board Science-Related Homework Help Mathematics
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tony tony
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11 years ago
Calculus:

How come you don't use the quotient rule here:

lnx/cscx

The answer is: 1/x divided by -cscxcotx....

What happened to the quotient rule?
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4 Replies
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wrote...
#1
11 years ago
you can use the quotient rule, but it is easier to notice that

lnx / cscx = lnx * sinx

and then use the product rule
wrote...
#2
11 years ago
You are trying to find the limit x->0 for the function
f(x) = lnx/cscx
The answer should be a value.

1/x divided by -cscxcotx.
1/x divided by -cosx/sinxsinx
=sinx/x * -1 sinx/cosx
= sinx/x * - tanx
As limit x->0
= 1 * tan 0 = 0

You are not finding f'(x), the derivative of the function, or the slope of the function, which is an equation of a function.
wrote...
#3
11 years ago
I assume you want to find the derivative since you mention the  quotient rule. You can write the expression as y = sinx(lnx) and use the product rule to write  dy/dx=sin(x)*(1/x) + ln(x)*(cosx)  which also does not simplify to the answer you have. Probaby the answer you were given is not correct. Or you were not asked for the derivative. Re-read the problem.
Answer accepted by topic starter
riya3rgriya3rg
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#4
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11 years ago
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