2.5 Implicit Differentiation

Implicit DIfferentiation Previous rules such as the product, quotient, power, and chain were only able to be applied to functions written in explicit form. Explicit form is when y is written as a function of x. When a function is not written explicitly you can either change the function to explicit form or use implicit differentiation. Explicit Form y = 1/x Implicit Form xy =1

2.5 Implicit Differentiation Solve for y

2.5 Implicit Differentiation

Take the derivative of each term, with respect to x Bring the dy/dx terms left, all other terms right. Factor out and solve for dy/dx. Slope

2.5 Implicit Differentiation Can't solve for y... So solve for x. Graph it... Slope

Always use this Tstep

Derivative

2.5 Implicit Differentiation Degenerate Circle

2.5 Implicit Differentiation Unit Circle Vertical Tangents

2.5 Implicit Differentiation Solve for y... ?

2.5 Implicit Differentiation

2.5 Implicit Differentiation Not in terms of x implies chain rule

2.5 Implicit Differentiation Rotate 90 degrees Parametric Mode Reflect over y

2.5 Implicit Differentiation

2.5 Implicit Differentiation 2.5/3,5,7,11,13,15,19,21,24,25,29,32,35,38,41,45,49,53,57