Course:MATH102/Question Challenge/2002 December Q2(iii)

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Question

Multiple choice:

The derivative of $y=\tan(x)$ at $x=\pi /4$ is

(a) -1 (b) 1 (c) 1/2 (d) 2 (e) 0

Hints

[show]Hint
Think of another way to represent the function tan in terms of sin and cos

Solutions

[show]Solution
$y=\tan(x)$ To find $dy/dx$ when $x=\pi /4$ we take the first derivative: $dy/dx=\sec ^{2}(x)$ We then substitute in our given value for x and simplify: $dy/dx=\sec ^{2}(\pi /4)$ $dy/dx=1/\cos ^{2}(\pi /4)$ $dy/dx=1/(({\sqrt {(}}{2})/({2}))^{2})$ $dy/dx=1/(1/2)$ $dy/dx=2$ The correct answer is D