Derivative – what is wrong in my calculation ?

[tedhill]

I started learning calculus. I am in the derivatives stage.

I am following the book “Calculus Demystified”. However I don’t understand the result of the derivative of [ e^x^2].

( ^ means raised to the power )

In my calculation I did this:

If (f ◦ g)(x) = e^x^2 and f(s) = s^2

Considering that ((f ◦ g)(x))’ =[ df/ds(g(x))].d/dx(f(x))

then ((f ◦ g)(x))’ = 2(e^x) . (e^x) = 2e^2x


But the book says that the resulting derivative is 2x.e^x^2.

If the book is correct, could someone explain how this derivative was calculated ?

[zaza]

Welcome to the Forums


If f is a function of s and s is a function of x, then:

df/dx = df/ds . ds/dx

Let's say f(s) = e^s

and s(x) = x²

i.e. f(x) = e^x2

Then df/ds = e^s - that's how the exponential behaves

ds/dx = 2x

So df/dx = 2xe^x2





What you are doing is considering the derivative of (e^x)², which is equivalent to taking the derivative of e^2x, and that as you have correctly pointed out is 2e^2x.


Make sense?



zaza