Question

How do you know which rule of differentiation to use?

Answer 1

Explanation:

We only need to be aware of the function.

One thing to keep in mind is that the derivative of a sum is the sum of the derivatives, allowing you to differentiate each component separately if you have additional terms.

Constant Rule	$\frac{d}{dx}C=0$
Power Rule	$\frac{d}{dx}{x}^n=n{x}^{n-1}$
Product Rule	$\frac{d}{dx}\left[f\left(x\right)g\left(x\right)\right]=f\left(x\right)g\text{'}\left(x\right)+f\text{'}\left(x\right)g\left(x\right)$
Quotient Rule	$\frac{d}{dx}\left[\frac{f\left(x\right)}{g\left(x\right)}\right]=\frac{g\left(x\right)f\text{'}\left(x\right)-f\left(x\right)g\text{'}\left(x\right)}{{\left[g\left(x\right)\right]}^2}$
Chain Rule	$\frac{d}{dx}f\left(g\right(x\left)\right)=f\text{'}\left(g\right(x\left)\right)g\text{'}\left(x\right)$