undefined To use implicit differentiation to isolate \( \frac{dy}{dx} \) in an equation, follow these steps: 1. Differentiate both sides of the equation with respect to \( x \). 2. Treat \( y \) as a function of \( x \) and apply the chain rule whenever you encounter \( y \). 3. After differentiation, isolate \( \frac{dy}{dx} \) on one side of the equation. 4. If possible, solve for \( \frac{dy}{dx} \) to express it explicitly in terms of \( x \) and/or \( y \).

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How do you use implicit differentiation to isolate dy/dx in this equation?

4sin(x-y)=4ysinx

Answer 1

Ezekiel Alexander

#(4cos(x-y)-4ycosx)/(4sinx+4cos(x-y)) = dy/dx#

#4sin(x-y)=4ysin x#

#4cos(x-y)-4cos(x-y)dy/dx = 4ycosx+4sinxdy/dx#

#4cos(x-y)-4ycosx=4sinxdy/dx+4cos(x-y)dy/dx#

#4cos(x-y)-4ycosx=(4sinx+4cos(x-y))dy/dx#

#(4cos(x-y)-4ycosx)/(4sinx+4cos(x-y)) = dy/dx#

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Answer 2

Emma Aldridge

To use implicit differentiation to isolate ( \frac{dy}{dx} ) in an equation, follow these steps:

Differentiate both sides of the equation with respect to ( x ).
Treat ( y ) as a function of ( x ) and apply the chain rule whenever you encounter ( y ).
After differentiation, isolate ( \frac{dy}{dx} ) on one side of the equation.
If possible, solve for ( \frac{dy}{dx} ) to express it explicitly in terms of ( x ) and/or ( y ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.