Differentiable functions is true or false?

 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).

2 Answers

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  • fcas80
    Lv 7
    1 month ago
    Favorite Answer

    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.

  • rotchm
    Lv 7
    1 month ago

    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). 

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