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.
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These are the problems (Please, just point me in the right direction):

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

f(x)=x\ln(12x)
 
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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).
 
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