Determine whether the statement is true or false.

Question

If f and g are differentiable, then d/dx [f(x)+g(x)]=f'(x)+g'(x)

Answer 1

True.

[f(x)+g(x)]' = f'(x) +g'(x)

try an example,

f(x) = x^2

g(x) = 2x

sum = x^2 + 2x

derivative = 2x +2 which is just the sum of the derivatives of each function