🐸 Froge's Guide to Differentiation 🐸

Understanding the Basics

Differentiation is a crucial concept in calculus which involves finding the derivative of a function. Derivatives represent how a function changes as its input changes, akin to how the froges gracefully leap from lily pad to lily pad.

Key Rules of Differentiation

• Power Rule: If \( f(x) = x^n \), then \( f'(x) = nx^{n-1} \).
• Product Rule: If \( u \) and \( v \) are functions of \( x \), then \( (uv)' = u'v + uv' \).
• Quotient Rule: If \( u \) and \( v \) are functions of \( x \), then \( \left(\frac{u}{v}\right)' = \frac{u'v - uv'}{v^2} \).
• Chain Rule: If a function \( y = f(g(x)) \), then \( \frac{dy}{dx} = f'(g(x))g'(x) \).