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You can do it!!!

2.5 Implicit Differentiation. You can do it!!!. How would you find the derivative in the equation x 2 – 2y 3 + 4y = 2 where it is very difficult to express y as a function of x?. To do this, we use a procedure called implicit differentiation. This means that when we differentiate terms

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You can do it!!!

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  1. 2.5 Implicit Differentiation You can do it!!!

  2. How would you find the derivative in the equation x2 – 2y3 + 4y = 2 where it is very difficult to express y as a function of x? To do this, we use a procedure called implicit differentiation. This means that when we differentiate terms involving x alone, we can differentiate as usual. But when we differentiate terms involving y, we must apply the Chain Rule. Watch the examples very carefully!!!

  3. Differentiate the following with respect to x. 3x2 2y3 x + 3y xy2 6x 6y2 y’ 1 + 3y’ x(2y)y’ + y2(1) = 2xyy’ + y2 Product rule

  4. Find dy/dx given that y3 + y2 – 5y – x2 = -4 Isolate dy/dx’s Factor out dy/dx

  5. What are the slopes at the following points? (2,0) (1,-3) x = 0 (1,1) undefined

  6. Determine the slope of the tangent line to the graph of x2 + 4y2 = 4 at the point . -2 -1 1 2

  7. Differentiate sin y = x Product Rule Differentiate x sin y = y cos x x cos y (y’) + sin y (1) = y (-sin x) + cos x (1)(y’) x cos y (y’) - cos x (y’) = -sin y - y sin x y’(x cos y - cos x) = -sin y - y sin x

  8. Given x2 + y2 = 25, find y” Now replace y’ with Multiply top and bottom by y What can we substitute in for x2 + y2?

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