Patrick Jones - Calculus - 1001 Practice Problems For Dummies (+ Free Online Practice)

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405–407Find the equation of the normal line at the indicated point.

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Chapter 7

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 4and 5) when finding derivatives.

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

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 finding the second derivative of an implicitly defined function, substitute in the first derivative in order to write the second derivative in terms of x and y.

When you substitute the first derivative into the second derivative, be prepared to further simplify.

408–413Use implicit differentiation to find .

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414–417Use implicit differentiation to find .

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418–422Find the equation of the tangent line at the indicated point.

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