- #1
Muthumanimaran
- 81
- 2
I don't knowSimon Bridge said:Do you know why they bothered to work out f(x+Δx)−f(x)f(x+\Delta x) - f(x) at all?
I mean: what's the point?
yes, derivative is the rate of one function to another function, it actually says how fast one function changes with respect to other, am I right?Simon Bridge said:How would you normally go about proving the product rule - if you didn't have the example from Riley and Hobson?
i.e. do you know the definition of the derivative?
Not exactly ... that was the description of what the derivative is, not the definition. The definition is: $$f^\prime(x) = \lim_{\Delta x\to 0}\frac{f(x+\Delta x) - f(x)}{\Delta x}$$ ... this gives the derivative of f(x) with respect to x.yes, derivative is the rate of one function to another function, it actually says how fast one function changes with respect to other, am I right?
got it. Thank youSimon Bridge said:Not exactly ... that was the description of what the derivative is, not the definition. The definition is: $$f^\prime(x) = \lim_{\Delta x\to 0}\frac{f(x+\Delta x) - f(x)}{\Delta x}$$ ... this gives the derivative of f(x) with respect to x.
To prove the product rule, first set ##f(x)=v(x)u(x)## then apply the definition to f.