Evaluate lim h->0 e^(x+h)^2 - e^x^2 / h by recognizing it as the derivative of ...

Question

Evaluate lim h->0 e^(x+h)^2 - e^x^2 / h by recognizing it as the derivative of a known function and applying a differentiation rule. For full credit you must clearly identify the function before applying any differentiation rules.

Answer 1

f'(x) = lim_h→0 [(f(x+h) - f(x)) / h

So, the given limit is f'(x) for f(x) = e^{x^2}.

Therefore, the value of the limit is f'(x) = 2xe^{x^2}