d/dx[e^x]
To find the derivative of the function f(x) = e^x, we can use the chain rule
To find the derivative of the function f(x) = e^x, we can use the chain rule.
The chain rule states that if we have a composition of functions, such as f(g(x)), then the derivative of this composition with respect to x is given by the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function with respect to x.
In this case, the outer function is f(x) = e^x and the inner function is g(x) = x.
Applying the chain rule, we find that:
d/dx[e^x] = d/dg[e^g] * dg/dx
The derivative of e^g with respect to g is simply e^g.
The derivative of g(x) = x with respect to x is 1.
So, putting it all together, we have:
d/dx[e^x] = e^x * 1
Therefore, the derivative of e^x with respect to x is simply e^x.
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