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If f(x)=4arctan(7x), find f'(x). Find f'(4).

User Yik
by
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1 Answer

7 votes

f'(x) = (4 arctan(7x))'

f'(x) = 4 (arctan(7x))'

By the chain rule,

f'(x) = 4/(1 + (7x)^2) * (7x)'

f'(x) = 28/(1 + 49x^2)

and hence

f'(4) = 28/(1 + 49*16) = 28/785

In case you're not sure about the derivative of arctan: If y = arctan(x), then x = tan(y). Differentiating both sides with respect to x gives

1 = sec^2y y' = (1 + tan^2y) y' = (1 + x^2) y'

==> y' = 1/(1 + x^2)

User Tanaka Mawere
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