calculus! TRUE OR FALSE. if f and g are differentiable then d/dx [f(x)+g(x)]=f'(x)+g'(x) ?

Question

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

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

Answer 1

True

False

True

Answer 2

It is vital that you know the answer to these questions if you are going to learn calculus, so I am not going to answer them for you.



if f and g are differentiable then d/dx [f(x)+g(x)]=f'(x)+g'(x) -- what do you think? Go back to the definition of differentiation... does this hold?



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

Read the product rule. Does this follow the product rule?



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

Read the chain rule. Does this follow the chain rule?

Answer 3

If f and g are differentiable then d/dx [f(x)+g(x)]=f'(x)+g'(x) (this is known as the sum rule)

If f and g are differentiable, then d/dx [f(x)g(x)] = f'(x)*g(x) + f(x)*g'(x) (this is known as the product rule)

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



The first one is true, the second one is false and the third one is true because I think you mistyped it.