Implicit Differentiation

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Presentation transcript:

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

Ex. If , find .

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

Ex. If , find .

Ex. Find the coordinates of any point on x2 + y2 = 16 where the tangent line has the slope of -1.

Ex. Let f (x) = x3 + x. If g(x) = f -1(x), find g(10).