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Maddie G

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# Which derivative rule would I use?

if I know the derivative of sine and cosine I could find the derivative directly of the tangent with what rule?

Chain? power? Product? or quotient?

### 2 Answers

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- PhilipLv 65 months agoFavorite Answer
1) Quotient rule: {d/dx}(u/v) = (1/v^2)[v(du/dx) - u(dv/dx)]. For tan = sin/cos we

have u = sin and v = cos, (du/dx) = cos, (dv/dx) = -sin. Then {d/dx}(tan) =;

(1/cos^2)[cos(cos) -sin(-sin)] = 1/cos^2 = sec^2.

2) Product rule combined with chain & power: We write tan = sin*cos^-1. Then u = sin & v = cos^-1. {d/dx}(u*v) = [u(dv/dx) + v(du/dx)]. (dv/dx) = -cos^-2(-sin).

(du/dx) = cos. Then {d/dx}(tan) = [sin(sincos^-2) + (cos^-1)cos] = 1+sin^2/cos^2

= (sin^2+cos^2)/cos^2 = 1/cos^2 = sec^2.

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