Question

Which one of the following statements is true?

Answer 1

Hi,

1) False, why ?

$Let\;say\;that:f(x)=x^2\;and\;g(x)=2x\\\\\dfrac{d}{dx}(f(x)\times g(x))=\dfrac{d}{dx}(x^2\times2x)=\dfrac{d}{dx}(2x^3)=3\times3x^2=6x^2\\\\But:f'(x)\times g'(x)=2x\times 2=4x\\\\6x^2\neq4x$

2) True, why ?

$\dfrac{d}{dx}|x^2+x|=\dfrac{d}{dx}(x^2+x)=2x+1$

3) False, I let you search ;)

4) We say that 2) was true, so.