Question

What is differentiation in simple words?

Answer 1

Differentiation

• Differentiation is the process of finding the derivative of a function.
• It can also be defined as the process of finding the rate of change of a function with respect to its variables.
• It is usually denoted as $\frac{dy}{dx}$, where $y=f\left(x\right)$

Some of the basic rules of derivation are:

1. The derivative of a constant is zero.
2. Power rule: $\frac{d}{dx}\left(x^n\right)=n{x}^{n-1}$
3. Multiplication constant: $\frac{d}{dx}\left[cf\left(x\right)\right]=c·\frac{d}{dx}f\left(x\right)$
4. Sum rule: $\frac{d}{dx}\left[f\left(x\right)+g\left(x\right)\right]=\frac{d}{dx}f\left(x\right)+\frac{d}{dx}g\left(x\right)$
5. Difference rule: $\frac{d}{dx}\left[f\left(x\right)-g\left(x\right)\right]=\frac{d}{dx}f\left(x\right)-\frac{d}{dx}g\left(x\right)$
6. Product rule: $\frac{d}{dx}\left[f\left(x\right)·g\left(x\right)\right]=\left[f\left(x\right)·\frac{d}{dx}g\left(x\right)\right]+\left[g\left(x\right)·\frac{d}{dx}f\left(x\right)\right]$
7. Quotient rule: $\frac{d}{dx}\left[\frac{f\left(x\right)}{g\left(x\right)}\right]=\frac{\left[g\left(x\right)·\frac{d}{dx}f\left(x\right)\right]-\left[f\left(x\right)·\frac{d}{dx}g\left(x\right)\right]}{{\left[g\left(x\right)\right]}^2}$