Identify any general rules of calculus that you use

i) f(x) = tan(3x)In(sin(3x))

ii) f(x) = e^-sqrt(x) divided by x^3 +1

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- Jul 10th 2006, 04:59 AMfair_lady0072002Differentiate each - please help
Identify any general rules of calculus that you use

i) f(x) = tan(3x)In(sin(3x))

ii) f(x) = e^-sqrt(x) divided by x^3 +1 - Jul 10th 2006, 06:26 AMgalactus
For the first, use the product rule:

First times derivative of second plus second times derivative of first.

I'll let you tidy it up a bit. - Jul 10th 2006, 06:54 AMmalaygoel
Here is second.

Your function is

Its differentiation is(using quotient rule)

It may be useful to you:

If u,v,w,... are functions of x then

Keep Smiling

Malay - Jul 10th 2006, 07:19 AMSoroban
Hello, fair_lady0072002!

Quote:

Identify any general rules of calculus that you use

We have: . . . . product rule

. . . . . . . . . . . chain rule

Simplify: .

. . . . . . . . . . . . . . reciprocals

Therefore: .

Quote:

This one is*truly messy!*

We have: .

Then: . . . . quotient rule

. . . chain rule

Now we simplify . . .*(do we hafta?)*

We have: .

Multiply top and bottom by

Therefore: .

[Disclaimer: not responsible for egregious errors.]

- Jul 11th 2006, 02:57 PMfair_lady0072002
Thanx a lot. I really appreciate your assistance.