# How do you differentiate #g(u)=sqrt2u+sqrt(3u)#?

If we want to use just the power rule (no chain rule) we'll rewrite

Therefore,

Note

I understand that, early on, there seem to be a lot of differentiation rules to memorize, but I suggest eventually memorizing this one also. The square root arises in many problems. (This is largely because of the Pythagorean Theorem. If we know distances in perpendicular directions, then we use the square root to find the straight line distance.)

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To differentiate g(u) = √(2u) + √(3u), you can use the chain rule:

g'(u) = (1/2)(2u)^(-1/2) * 2 + (1/2)(3u)^(-1/2) * 3

Simplify:

g'(u) = u^(-1/2) + (3/2)u^(-1/2)

Combine like terms:

g'(u) = (1 + 3/2)u^(-1/2)

Simplify further:

g'(u) = (5/2)u^(-1/2)

So, the derivative of g(u) with respect to u is g'(u) = (5/2)u^(-1/2).

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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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