Warm up Problems 1. 2. 3.. Implicit Differentiation Ex. So far, all problems have been y = f (x)  What if x’s and y’s are mixed together?

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Presentation transcript:

Warm up Problems

Implicit Differentiation Ex. So far, all problems have been y = f (x)  What if x’s and y’s are mixed together?

Ex. If cos x + y 2 – y = x, find. Steps for Implicit Differentiation Derivative of x-function is the same as usual. Derivative of y-function gets. If x’s and y’s mixed, use product rule. Solve for.

Ex. If cos x + y 2 – y = x, find.

Ex.

Pract.

Ex. Find the slope of the line tangent to y = x + cos(xy) at the point where x = 0.

Ex. If cos x + y 2 – y = x, find.

Ex. Find the coordinates of any point on x 2 + y 2 = 16 where the tangent line has the slope of -1.

Ex. Let f (x) = x 3 + x. If g(x) = f -1 (x) and g(10) = 2, find g(10).

Next class, you will be taking a Derivative Quiz