Question

The derivative of sum or difference of two functions is the product of derivatives of those two functions.

• A. True
• B. False

Answer 1

The correct option is B False

We have discussed in the videos that if let’s say f(x) and g(x) are two functions of x, then the derivative of their sum i.e.,
$\frac{d}{dx}\left(f\right(x)+g(x\left)\right)$ will be equal to the sum of derivatives of two fnctions. i.e., $\frac{d}{dx}\left(f\right(x\left)\right)+\frac{d}{dx}g\left(x\right)).$
Same rule holds with difference as well i.e., $\frac{d}{dx}\left(f\right(x)-g(x\left)\right)=\frac{d}{dx}\left(f\right(x\left)\right)-\frac{d}{dx}\left(g\right(x\left)\right).$ We can prove it by using first principle as well. You should try this on your own.