i have two questions, for both i need to find F'(x) of the function.

i think both are using the product rule but not 100% certain. All help much appreciated.

1 f(x)= ln(x^3-1/3x^2)

2 f(x)=e^cosx *sin(ln x)

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- Jun 29th 2008, 01:31 AMolliemanDifferential calculus
i have two questions, for both i need to find F'(x) of the function.

i think both are using the product rule but not 100% certain. All help much appreciated.

1 f(x)= ln(x^3-1/3x^2)

2 f(x)=e^cosx *sin(ln x) - Jun 29th 2008, 01:59 AMwingless
1. Use chain rule and quotient rule.

2. Use chain rule and product rule. - Jun 29th 2008, 02:28 AMSimplicity
- Jun 29th 2008, 03:10 AMnikhilCheck this out
Hi!ollieman

Chain rule should be used for sureand

I will solve one of the question

as an example.(you may do other one by urself,ask if you have any doubt in solving)

y=f(x)=[e^cosx]sin(ln(x))

differentiating we get

y'=[d/dx(e^cosx)]sin(ln(x))+[e^cosx]d/dx(sin(lnx))

y'=[d/dx(e^cosx)]sin(ln(x))+[e^cosx]cos(lnx)d/dx(lnx)

y'=[d/dx(e^cosx)]sin(ln(x))+[e^cosx]cos(lnx)(1/x)

we may solve [d/dx(e^cosx)] saperately as it is a power function

let A=e^cosx

lnA=cosx

1/A(dA/dx)=-sinx

dA/dx=-sinx*A=-e^cos(x)[sin(x)]

so finally

y'= -[e^cos(x)]sin(x)sin(lnx)+[e^cosx]cos(lnx)(1/x)