Implicit Differentiation Niagara Falls, NY & Canada Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003.

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Presentation transcript:

Implicit Differentiation Niagara Falls, NY & Canada Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003

Reminders: Chain rule Notation

Reminders: Chain rule Notation

Reminders: Chain rule Notation

Implicit Function An implicit function is one that cannot be easily manipulated to the form y = f(x).

This is not a function, but it would still be nice to be able to find the slope.

Do the same thing to both sides.

This is not a function, but it would still be nice to be able to find the slope. Do the same thing to both sides.

This is not a function, but it would still be nice to be able to find the slope. Do the same thing to both sides. Note use of chain rule.

This is not a function, but it would still be nice to be able to find the slope. Do the same thing to both sides. Note use of chain rule.

This is not a function, but it would still be nice to be able to find the slope. Do the same thing to both sides. Note use of chain rule.

This is not a function, but it would still be nice to be able to find the slope. Do the same thing to both sides. Note use of chain rule.

This is not a function, but it would still be nice to be able to find the slope. Do the same thing to both sides. Note use of chain rule.

This technique is called implicit differentiation. 1 Differentiate both sides w.r.t. x. 2 Solve for.

This technique is called implicit differentiation. 1 Differentiate both sides w.r.t. x. 2 Solve for.

This can’t be solved for y. This technique is called implicit differentiation. 1 Differentiate both sides w.r.t. x. 2 Solve for.

This can’t be solved for y. This technique is called implicit differentiation. 1 Differentiate both sides w.r.t. x. 2 Solve for.

This can’t be solved for y. This technique is called implicit differentiation. 1 Differentiate both sides w.r.t. x. 2 Solve for.

This can’t be solved for y. This technique is called implicit differentiation. 1 Differentiate both sides w.r.t. x. 2 Solve for.

This can’t be solved for y. This technique is called implicit differentiation. 1 Differentiate both sides w.r.t. x. 2 Solve for.

This can’t be solved for y. This technique is called implicit differentiation. 1 Differentiate both sides w.r.t. x. 2 Solve for.

Find dy/dx given that y 3 + y 2 – 5y – x 2 = -4

Find dy/dx given that y 3 + y 2 – 5y – x 2 = -4

Find dy/dx given that y 3 + y 2 – 5y – x 2 = -4 Isolate dy/dx’s

Find dy/dx given that y 3 + y 2 – 5y – x 2 = -4 Isolate dy/dx’s

Find dy/dx given that y 3 + y 2 – 5y – x 2 = -4 Isolate dy/dx’s Factor out dy/dx

Find dy/dx given that y 3 + y 2 – 5y – x 2 = -4 Isolate dy/dx’s Factor out dy/dx

Find dy/dx given that y 3 + y 2 – 5y – x 2 = -4 Isolate dy/dx’s Factor out dy/dx

Determine the slope of the tangent line to the graph of x 2 + 4y 2 = 4 at the point

Determine the slope of the tangent line to the graph of x 2 + 4y 2 = 4 at the point

Determine the slope of the tangent line to the graph of x 2 + 4y 2 = 4 at the point

Determine the slope of the tangent line to the graph of x 2 + 4y 2 = 4 at the point

Determine the slope of the tangent line to the graph of x 2 + 4y 2 = 4 at the point

Determine the slope of the tangent line to the graph of x 2 + 4y 2 = 4 at the point

Determine the slope of the tangent line to the graph of x 2 + 4y 2 = 4 at the point

Determine the slope of the tangent line to the graph of x 2 + 4y 2 = 4 at the point

Find the equation of the line tangent to the curve at.