MATH 1010U Lecture Notes - Lecture 5: Natural Logarithm, Hyperbolic Function, Inverse Trigonometric Functions
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Find y . explicitly, but what if y is defined implicitly. Problem: most implicit relationships are too hard to isolate for y. Steps: differentiate both sides with respect to x. (keep in mind that y is a function of x. , solve for y . Example: find the slope of the tangent line at ( x. Application: the relationship between the number of species in a genus (x) and the yx a where a and k are number of genera (y) comprising x species is given by constants. [source: calculus for the life sciences , by r. greenwell, n. ritchey, and m. lial, 2003] dy . dx k. Exercise (application): the demand function for a certain commodity is given by. 500000 p where p is the price in dollars and q is the demand in hundreds of units. Find the rate of change of demand with respect to price when q = 100 (that is, find dq . ) dp.
