Computing Derivatives Exercises

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• This function is a line with slope 3, therefore f ' (x) = 3. Alternately, we can find the derivatives of the terms and add those together:

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• We find the derivatives of the terms and add:

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• First we rewrite the function:

Now we can take the derivative:

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• This is a trick question. Although there's a π and an e and a natural log and a square root, there aren't any x's in the expression

This function is a complicated constant, therefore its derivative is 0.

f ' (x) = 0

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• The first thing to do is make the function look better and turn the log₂ x into :

Now we can take the derivative without too much fuss:

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• First we rewrite the function:

Then we take the derivative:

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• There are no x's in the expression

therefore this is another complicated constant. The derivative of a constant is 0, therefore

f ' (x) = 0.

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• First we rewrite the function:

All of a sudden the function is simplified f(x) = 6x – 1 which describes a straight line with a slope of 6, therefore

f ' (x) = 6.