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.
Example 7
Find the derivative of the function.
f(x) = 10sin x
Answer
f ' (x) = 10(sin x)' = 10(cos x)
Example 8
Find the derivative of the function.
g(x) = 6ex
Answer
g ' (x) = 6(ex)' = 6(ex) = 6ex
Example 9
Find the derivative of the function.
g(x) = 4(5)x
Answer
g ' (x) = 4 · ( 5x)' = 4(5xln 5) = (4 ln 5)5x. There's no particularly tidy way to write this answer.
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