Online Derivative Calculator ? Shows All Steps!
My derivative calculator says to apply the generalized product rule so that:
At first I thought it looked kind of like the chain rule however x^x is not the derivative of x^x. The answer output by the derivative calculator matches my solutions manual but I don't understand the steps I think.
Thanks for any responses...
P.S. I the calculator just means the product rule then I am still confused about ln(x) and how ln(x) became a part of the equation.
So the derivative of is
I am seeing the chain rule as:
Is that above not correct?
I am trying to see how that might be similar to:
The:
is confusing because I don't see that above as a derivative.
Thanks for any responses...
Thank you for clearing that up. I believe that is true but I am still confused about something. From what I know about the chain rule it is the derivative of the whole part multiplied by the derivative of the inside.
Example:
https://www.math.ucdavis.edu/~kouba/....html#SOLUTION1
In the case my question is that does not appear to be a derivative in this case. So clearly is a derivative but does not look like one. Is there something I don't understand maybe about the chain rule?
Thanks for any responses....
it might be clearer if you thought of the example about as follows.
d/dx((3x+1)^{2}) = d/dx(u^{2}) where u = 3x+1
d/dx(u^{2}) = d/du(u^{2}) du/dx = 2u * 3 = 2(3x+1)*3 = 6(3x+1)
Apply this thinking to your exponential example
d/dx (e^{f(x)})
let u = f(x) du/dx = f'(x)
d/dx(e^{u}) = d/du(e^{u}) du/dx = e^{u} f'(x) = e^{f(x)} f'(x)