How do you find #(dy)/(dx)# given #e^siny+y=x^2#?
Differentiate both sides. Recall that the chain rule will be put into effect.
This gives us:
Reapplying the chain rule:
Thus:
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To find (dy)/(dx) given e^siny + y = x^2, differentiate both sides of the equation with respect to x using implicit differentiation.
(e^siny)(dy/dx) + (dy/dx) = 2x
Now, solve for (dy/dx):
(dy/dx)(1 + e^siny) = 2x
(dy/dx) = 2x / (1 + e^siny)
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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.
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.
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.
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.
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