Computing Derivatives Exercises

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• f ' (x) = 1

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• g ' (x) = 2f ' (x) = 2

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• h(x) = 2g(x) = 2(2x) = 4x, therefore h ' (x) = 4.

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• k(x) = 2h(x) = 2(4x), therefore k ' (x) = 8.

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• f ' (x) = 5(x³)' = 5(3x²) = 15x²

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• f ' (x) = 6(cos x)' = 6(-sin x) = -6sin x. Parentheses are important here. If we didn't have them we might end with the answer 6 – sin x, which isn't correct.

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• f ' (x) = 10(sin x)' = 10(cos x)

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• g ' (x) = 6(e^x)' = 6(e^x) = 6e^x

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• g ' (x) = 4 · ( 5^x)' = 4(5^xln 5) = (4 ln 5)5^x. There's no particularly tidy way to write this answer.

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• Again, we start by rewriting the function:

Then we can find the derivative:

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• h ' (x) = 4(x¹²)' = 4(12x¹¹) = 48x¹¹