- #1
bob4000
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i have a question I'm attempting as extra work, I have tried the usual method but no luck... find expressionsf for dy/dx in terms of x and y:
ln(x^2+1) + ln(y+1) = x +y
ln(x^2+1) + ln(y+1) = x +y
Jeff Ford said:Remember [tex] \frac{d}{dx} \ln(x^2 +1) \neq \frac{1}{x^2+1} [/tex]
You need to use the chain rule to get the proper derivative.
The formula for differentiating natural logs of x and y functions is d/dx(ln(x)) = 1/x and d/dy(ln(y)) = 1/y.
The difference is that the derivative of natural logs of x and y functions is 1/x and 1/y, whereas the derivative of other logarithmic functions involves using the chain rule.
No, the power rule cannot be used to differentiate natural logs of x and y functions. Instead, the formula d/dx(ln(x)) = 1/x and d/dy(ln(y)) = 1/y should be used.
Yes, it is possible to differentiate natural logs of x and y functions with respect to a different variable. The formulas d/dx(ln(x)) = 1/x and d/dy(ln(y)) = 1/y can be used for any variable.
Natural logs of x and y functions are commonly used in finance, biology, and physics. For example, in finance, natural logs are used to calculate compound interest and in biology, natural logs are used to model population growth. In physics, natural logs are used to model radioactive decay.