How do you use the quotient rule to find the derivative of $y=tan(x)$ ?

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Answer 1 · 2018-03-06T09:54:18

Kindly refer to the Explanation.

$"The Quotient Rule for Differentiation : "(u/v)'=(vu'-uv')/v^2$ .

$:. d/dx(tanx)=(sinx/cosx)'$ ,

$={cosx*(sinx)'-sinx*(cosx)'}/(csx)^2$ ,

$={cosx*cosx-sinx(-sinx)}/cos^2x$ ,

$={cos^2x+sin^2x}/cos^2x$ ,

$=1/cos^2x$ .

$rArr (tanx)'=sec^2x$ .

How do you use the quotient rule to find the derivative of y=tan(x)y=tan(x) ?