Review for Derivative Test

Implicit Derivatives

100

Find dy/dx of 

3x=y^2+7

dy/dx=3/(2y)

200

Find dy/dx of 

12x^2=y^2+5y

dy/dx=(24x)/(2y+5)

300

Which part of the equation, would you set equal to 0 to find vertical asymptotes? 

dy/dx=(x+3)/(y-2)

Denominator (y-2)

400

Find dx/dy of 

7y^2=2x^3

dx/dy=(14y)/(6x^2)=(7y)/(3x^2)

500

Find the second derivative at (1,2) of 

x^2+y^2=5

-5/8

Basic Derivative Rules

100

Find the derivative of 

y=7x+sqrtx-1/(x^4)

y'= 7+1/2x^-(1/2)+4x^-5

200

Find the derivative of 

y=e^(4x^5)

y'= 20x^4e^(x^5)

300

Find the derivative of 

y=sec(x^3)

y'=3x^2sec(x^3)tan(x^3)

400

Find derivative of 

y=6^sinx

y'=(cosx)6^sinxln6

500

Find derivative of 

y=3log_5(x+1)

y'=3/(ln5(x+1))

Complex Derivative Rules

100

Find the derivative of 

y=xe^x

y=xe^x+e^x

200

Find the derivative of 

y=tanx/(x^2)

y'=(x^2sec^2(x)-2xtanx)/x^4

300

Find the derivative of 

y=sqrt(x^5+9x-1)

y'=(5x^4+9)/(2sqrt(x^5+9x-1)

400

Find the derivative of the following 

y=cos^3(x^2+1)

y'=-6xcos^2(x^2+1)sin(x^2+1)

500

Find the derivative of 

y=tan^2(sin(x^3))

6x^2tan(sin(x^3))sec^2(sin(x^3)cos(x^3)

L'hopital Rule

100

lim_(x->-5)(x^2+x-20)/(x+5)

-9

200

lim_(x->oo)x/(e^x)

0

300

lim_(x->0)xcotx

1

400

lim_(x->oo)x^(1/x)

1

500

lim_(x->oo)x^(1/lnx)

e

Hodge Podge

100

Find the tangent line at x=2 to 

y=x^2+7x-1

(y-17)=11(x-2)

200

If f(1) = 4 and f'(1) = 8 and f'(4) = 7 and g is the inverse of f, find g'(4).

1/8

300

Find the values of a and b to make the function differentiable at x=1

{(ax^2 +6),(bx-2):} 

 

a = 8 and b=16

400

A tangent line through the point (1, 5) is y=5.  What is the equation of the normal line?

x=1

500

List the 5 indeterminate forms of L'hopital's Rule

0*oo, oo-oo, 1^oo, oo^0, 0^0