MATH 1300 Study Guide - Quiz Guide: Algebraic Function, Inverse Trigonometric Functions

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1 Oct 2018
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MATH 1300 Full Course Notes
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Name: what are the derivatives of the following functions? (you should know all of these!) (a) ln x and log3 x. In general (c) tan x and arctan x: find the derivative of (ln x)(cid:48) = 1 x ln a (ex)(cid:48) = ex, (3x)(cid:48) = 3x ln 3. (ax)(cid:48) = ax ln a. (tan x)(cid:48) = sec2 x, (arctan x)(cid:48) = 1 + x2 . y = sin(ln(3x2 + 2)) 3x2 + 2: use implicit di erentiation to nd the equation of the tangent line to the curve. 2(x2 + y2)2 = 25(x2 y2) going through the point (3, 1). Di erentiating both sides and assuming y is a di erentiable function of x we have. 4(x2 + y2)(2x + 2yy(cid:48)) = 25(2x 2yy(cid:48)). At (x, y) = (3, 1) we have y(cid:48) = 9/13. The equation of the line through (3, 1) with slope 9/13 is y 1 = (x 3).

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