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3.7 Implicit Differentiation. Example. Find dy/dx given x 2 + y = 3. First solve for y, then take derivative But what if you can’t solve for y?. Implicit Differentiation. Implicit Differentiation allows us to find dy/dx for an equation like that cannot be easily solved for y. Method.
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Example Find dy/dx given x2 + y = 3. First solve for y, then take derivative But what if you can’t solve for y?
Implicit Differentiation • Implicit Differentiation allows us to find dy/dx for an equation like that cannot be easily solved for y.
Method • Take the derivative with respect to x of every term on both sides. • Treat y as a function of x which means use the chain rule with y • Solve for dy/dx
Example • Find dy/dx given y2 = x
Example • Find dy/dx given
Example • Find dy/dx given
Example • Find dy/dx given
Example • Find dy/dx given
Example • Find dy/dx given
Example • Find the slope of at
Example • Find the slope of at
Example • Find the tangent to the curve at the point
Find the equations of the lines tangent and normal to the curve at . Note product rule.
Find if . Substitute back into the equation. Higher Order Derivatives
