Topic 03

Core Solving Rules

Mahir Shahariar Presented By Mahir Shahariar

"Thank you, Abrar. Finding limits manually for every equation is extremely time-consuming. To speed up the process, mathematicians derived some Core Shortcut Rules. Let's explore the most powerful tools in our calculus toolkit."

1. Constant Rule

The derivative of a constant number (like 5 or 100) is always zero, because a constant value never changes (slope is a flat line).

d/dx (c) = 0

2. The Power Rule

The most widely used rule. Bring the exponent down to the front as a multiplier, then subtract 1 from the exponent.

d/dx (xn) = n·xn-1

3. Sum & Difference

If you have multiple terms added or subtracted, simply differentiate each term individually.

d/dx (u ± v) = u' ± v'

Power Rule Visualizer

Change the exponent (n) to see how the Power Rule transforms the original function into its derivative.

f(x) = x² f'(x) = 2x
Set Exponent (n) = 2
Original Function, f(x)
x2
Derivative, f'(x)
2x1

"The Power and Sum rules are great for simple polynomials. But what if two functions are multiplying each other, or one is inside another? Ashraf will now explain Advanced Techniques."

Ashraf Uddin Apu: Advanced Techniques