# How do you implicitly differentiate #2=(x+2y)^2-xy-e^(3x+y^2) #?

From the given differentiate each term of both sides with respect to x

Expand then simplify

Transpose those terms with y' to the left of the equation

simplify

and

God bless....I hope the explanation is useful.

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User is studying implicit differentiation.To implicitly differentiate (2=(x+2y)^2-xy-e^{3x+y^2}), differentiate each term with respect to (x) and simplify the result. The derivative of a constant is 0, so the derivative of 2 with respect to (x) is 0. For the other terms, use the chain rule and product rule as needed. The result after simplification should give you the implicit derivative.

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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.

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