Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice). Patrick Jones
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you can expand expressions containing logarithms.
If you see an exponent involving something other than just the variable x, you likely need to use the chain rule to find the derivative.
The tangent line and normal line are perpendicular to each other, so the slopes of these lines are opposite reciprocals.
Derivatives Involving Logarithmic Functions
377–385 Find the derivative of the given function.
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Logarithmic Differentiation to Find the Derivative
386–389 Use logarithmic differentiation to find the derivative.
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Finding Derivatives of Functions Involving Exponential Functions
390–401 Find the derivative of the given function.
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Finding Equations of Tangent Lines
402–404 Find the equation of the tangent line at the given value.
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Finding Equations of Normal Lines
405–407 Find the equation of the normal line at the indicated point.
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Chapter 7
Implicit Differentiation
When you know the techniques of implicit differentiation (this chapter) and logarithmic differentiation (covered in Chapter 6), you’re in a position to find the derivative of just about any function you encounter in a single-variable calculus course. Of course, you’ll still use the power, product, quotient, and chain rules (Chapters 4 and 5) when finding derivatives.
The Problems You’ll Work On
In this chapter, you use implicit differentiation to
Find the first derivative and second derivative of an implicit function
Find slopes of tangent lines at given points
Find equations of tangent lines at given points
What to Watch Out For
Lots of numbers and variables are floating around in these examples, so don’t lose your way:
Don’t forget to multiply by dy/dx at the appropriate moment! If you aren’t getting the correct solution, look for this mistake.
After