SUMS

Theorem 3. The derivative of the sum of two or more differen­tiable functions of x is equal to the sum of their derivatives. If two functions of x are given, such that

u = g(x)

and

v = h(x)

and also

then

PROOF. -

and

Subtract equation (5.1) from equation (5.2):

Rearrange this equation such that

Divide both sides of the equation by Ax and then take the limit as :

But, by definition

and

Then by substitution,

EXAMPLE. Find the derivative of the function

SOLUTION: Theorem 3 indicates that we should find the derivative of each term and then show them as a sum; that is, if

and

then

PRACTICE PROBLEMS:

Find the derivative of the following:

ANSWERS:

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