Mastering Derivatives: Chain Rule, Implicit Differentiation, Logarithmic Functions
Learn how to tackle complex functions with the chain rule, solve implicit equations with differentiation, and derive logarithmic functions efficiently. Understand methods through clear examples.
Mastering Derivatives: Chain Rule, Implicit Differentiation, Logarithmic Functions
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Presentation Transcript
Sections 3.5 – 3.7 Michael London
Section 3.5 The Chain Rule • Some functions are difficult to derive because they may be a function within another function • To solve a derivative like this, always work from the outside to the inside, making sure to take the derivative of each part of the function. • EX:
Section 3.6 Implicit Differentiation • Some functions are defined by a relationship between x and y • Some of these equations may be hard to solve for y in order to easily integrate for just one value…so why not do it in terms of both? • For any term that has y or has something being done to the y, add a dy/dx (this simply means, derivative of y in respect to x) • Finally, isolate terms with dy/dx and solve for dy/dx
Section 3.7 Derivates of Logarithmic Functions • The derivate of a logarithmic function is simply : • The derivative of a natural log function is:
