Need help on finding derivatives of logarithmic functions

AI Thread Summary
To find the derivatives of the logarithmic functions y=x^2ln(6x) and f(x)=xln(12x), apply the product rule: d(uv)/dx = u'v + uv'. The derivative of ln(x) is 1/x, which is essential for these calculations. For y=x^2ln(6x), use the product rule and chain rule to differentiate appropriately. Understanding these rules is crucial for solving similar problems involving logarithmic functions.
jzq
Messages
54
Reaction score
0
These are the problems (Please, just point me in the right direction):

y=x^{2}\ln(6x)

f(x)=x\ln(12x)
 
Physics news on Phys.org
Do you know the derivative of ln(x)?
 
whozum said:
Do you know the derivative of ln(x)?
1/x

10 char
 
The product rule -- d(uv)/dx = u'v + uv'
[edit: sorry had the answers, didnt know he didnt want to know them]
 
Last edited:
y = x^2ln(6x)

\frac{dy}{dx} = \frac{d(x^2ln(6x))}{dx}

which is of the form

\frac{d(u(x)v(x))}{dx} = u\frac{dv}{dx} + v\frac{du}{dx}

Use the chain rule when necessary (in the logarithm).
 
I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
Thread 'A cylinder connected to a hanging mass'
Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
Back
Top