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

by OC2540294

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MathematicsCourse Code

MATH 1300Professor

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**preview**shows half of the first page. to view the full**2 pages of the document.**Math 1300-001, Quiz 5 Name:

1. What are the derivatives of the following functions? (You should know all of these!)

(a) ln xand log3x

(ln x)0=1

x,(log3x)0=1

xln 3.

In general

(logax)0=1

xln a.

(b) exand 3x

(ex)0=ex,(3x)0= 3xln 3.

In general

(ax)0=axln a.

(c) tan xand arctan x

(tan x)0= sec2x, (arctan x)0=1

1 + x2.

2. Find the derivative of

y= sin(ln(3x2+ 2))

y0= cos(ln(3x2+ 2)) 6x

3x2+ 2.

3. Use implicit diﬀerentiation to ﬁnd the equation of the tangent line to the curve

2(x2+y2)2= 25(x2

−y2)

going through the point (3,1).

Diﬀerentiating both sides and assuming yis a diﬀerentiable function of xwe have

4(x2+y2)(2x+ 2yy0) = 25(2x−2yy0).

Solving for y0we have

y0=50x−8x(x2+y2)

50y+ 8y(x2+y2).

At (x, y) = (3,1) we have y0=−9/13. The equation of the line through (3,1) with

slope −9/13 is

y−1 = −9

13 (x−3).

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