Find the derivative: f(x)=tan(x^(2) +5)

asked Feb 24, 2021 80.0k views

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Find the derivative:
f(x)=tan
(x^(2) +5)

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Answer:

$2x \sec^2 (x^2 + 5)$

Explanation:

$f(x) = \tan (x^2 + 5)$

$(d)/(dx) \tan u = \sec^2 u (d)/(dx) u$

$(d)/(dx) \tan (x^2 + 5) = \sec^2 (x^2 + 5) (d)/(dx) (x^2 + 5)$

$(d)/(dx) \tan (x^2 + 5) = [\sec^2 (x^2 + 5)]2x$

$(d)/(dx) \tan (x^2 + 5) = 2x \sec^2 (x^2 + 5)$

Tsimbalar answered Feb 28, 2021

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