Differentiable functions is true or false?

Question

 Assume f and g are differentiable functions. Are the following statements true or false?

(a) The derivative of [f(x)g(x)] is f '(x)g'(x). 

(b) The derivative of e^2 f(x) is e^2f '(x).

Answer 1

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a. Let's try f(x) =x^2, g(x) = e^x. f'(x) = 2x, g'(x) = e^x. f'(x)g'(x) = 2x e^x.

d/dx[x^2 * e^x] = 2x * e^x + x^2 * e^x. So a is false.

b. I assume you mean this as (e^2)*(f(x)). So e^2 is a constant. d/dx[(e^2)*f(x))] = (e^2) * f'(x). So b is true.

Answer 2

Hint: For these, YOU need to learn (by heart) the rules of differentiation. We can't go and learn by heart for you!

a) So, consult your documentation, and tell us here what is the multiplication rule for derivatives. 

Another way, is to actually try with asimple functions. 

E.g.: Use the two functions x & x. So is [x*x]' =? x' * x' 

b) again, you need to know by heart the derivative of e^u, u=u(x).