# How do you differentiate #sqrt(cos(x^2+2))+sqrt(cos^2x+2)#?

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To differentiate the expression sqrt(cos(x^2+2)) + sqrt(cos^2x + 2), you can use the chain rule. The derivative of sqrt(u) with respect to x is (1/2)*u^(-1/2)*du/dx. Applying this rule to each term, the derivatives are as follows:

For the first term: Derivative of sqrt(cos(x^2+2)) = (1/2)*(cos(x^2+2))^(-1/2) * derivative of (cos(x^2+2)) with respect to x.

For the second term: Derivative of sqrt(cos^2x + 2) = (1/2)*(cos^2x + 2)^(-1/2) * derivative of (cos^2x + 2) with respect to x.

To find the derivatives of the inner functions, you need to apply the chain rule and the derivative of cos(x) which is -sin(x). After finding the derivatives, simplify the expressions.

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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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