Thread: Differential 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)

1. Use chain rule and quotient rule.
2. Use chain rule and product rule.

Originally Posted by ollieman

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)

1.


Using the log rules:



is given if in a fraction, the denominator differentiated gives the numerator.




2.

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)