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How do you determine dy/dx given #x+siny=y+1#?

Answer 1

Christopher Allers

#dy/dx = 1/(1 - cosy)#

#d/dx(x + siny) = d/dx(y + 1)#

#d/dx(x) + d/dx(siny) = d/dx(y) + d/dx(1)#

#1 + cosy(dy/dx) = 1(dy/dx) + 0#

#1 = 1(dy/dx) - cosy(dy/dx)#

#1 = dy/dx(1 - cosy)#

#dy/dx = 1/(1 - cosy)#

Hopefully this helps!

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Answer 2

Samantha Adkison

To determine dy/dx given the equation x + sin(y) = y + 1, you can use implicit differentiation. First, differentiate both sides of the equation with respect to x. Then, solve for dy/dx. Here's the process:

Differentiate both sides of the equation with respect to x.
For the left side, the derivative of x with respect to x is 1. For the right side, use the chain rule to differentiate sin(y) with respect to x, which gives cos(y) * dy/dx.
Set the resulting expression equal to dy/dx.
Solve for dy/dx.

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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.