Derivatives Crash Course

A concise breakdown of how to find the instantaneous rate of change. Master these four fundamental slides to solve any polynomial derivative problem rapidly with total precision.

Module 01

Definition as Limit

Concept of slope at a point
Limit as h approaches 0
f'(x) = lim[h→0] (f(x+h)-f(x))/h
Example: f(x)=x² → f'(x)=2x

Module 02

Power & Constant Rules

d/dx(c) = 0 (Constant rule)
d/dx(xⁿ) = nxⁿ⁻¹ (Power rule)
(cf)' = cf' (Scale rule)
Example: d/dx(3x³) = 9x²

Module 04

Product & Quotient Rules

(fg)' = f'g + fg' (Product)
(f/g)' = (f'g - fg')/g² (Quotient)
Example: (x·(x+1))' = 2x+1
For complicated polynomial terms

Try, Check & Master: Step-by-Step Training

Solve one by one and check with AI. Try again if needed or unlock the full solution.

Easy

Foundational Basics

Find d/dx of x²
Find d/dx of 5x
Find d/dx of constant 3

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Medium

Core Mastery

Derive 3x³ - 2x
Apply rule to x⁴ + 5x
Solve 2x⁻² + 4

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Challenge

Advanced Synthesis

Product: (x²+1)(x-3)
Quotient: (x²)/(x-1)
Chain: √(x³ + 2)

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