Calculus Semester final review

Find the derivative: -9e^3x

-27e^3x

Find the derivative: (3x + 5)^2

18x + 30

Find the derivative: 3x(3x^2 - 7x)

27x^2 - 42x

derivative of secx

secxtanx

Find the horizontal tangents of the curve. y= x^2 - 18x + 82

x=9

Find the inverse of the function f(x) =3/(x-6)

y= 3/x + 6

Find the intervals on which the function is continuous. y=e^(1/x)

(- infinity, 0) (0, infinity)

Find the derivative: (sqrt(7+sin(4x)))

(2cos(4x))/(sqrt(7+sin(4x)))

Find (dy/dx): x^2 + y^2 - xy = 4

(2x-y)/ (-2y+x)

Find the derivative: ln[x(sqrt(2x + 1))]

(3x + 1)/(x(2x + 1))

Find the derivative: [(5x^5 - 3)/(-3x^3 + 1)]^3

(3x^2(5x^5 - 3)^2(-30x^5 + 25x^2 -27))/(-3x^3 + 1)^4

Rewrite the exponential expression to have the indicated base. 64^2x; base 4

(4^3)^2x

Find the derivative: sinx/6x

(x(cosx)-(sinx))/(6x^2)

Multiply. ((x^5/4) - (sqrt(3)))^2

(x^5/2) - (2(sqrt(3))x^5/4) + 3

Find the requested function value meeting all of the given conditions. tan (-) = 1 and sin (-) <0; Find sec (-)

-(sqrt(2))

Find the derivative: (x + 2)/ (x-2)

-4/(x-2)^2

Find the indicated trigonometric function, given that (-) is an angle in standard position with the terminal side passing through the given point. (-8,6); Find cot (-)

-4/3

Find the derivative: 5/sinx

-5cscx(cotx)

Find the limit. lim(x approaches negative infinity) (7x + cosx)/x

-7

Find the derivative: 14x(sqrt(cscx))

-7x(sqrt(cscx))(cotx) + 14(sqrt(cscx))

Find the limit. lim(x approaches negative infinity) (8x + 5)/(|x|)

-8

derivative of cotx

-csc^2x

derivative of cscx

-cscxcotx

derivative of cosx

-sinx

Find the derivative: 8^cosx

-sinx(8^cosx)(ln8)

Determine the limit algebraically, if it exists. lim(x approaches -10) (x^2 + 20x + 100)/ (x+10)

0

Give the measure of the angle in radians. Give an exact answer whenever possible. Round approximations to the nearest hundredth. sec^-1 (1)

0

Find the derivative: ln(ln 2x)

1/ (X(ln 2x))

derivative of arctan(x)

1/(1+x^2)

Find the derivative: arcsin(x/2)

1/(sqrt(4-x^2))

The position of a particle moving along a coordinate line is s=(sqrt(2 + 2t)), with s in meters and t in seconds. Find particle's velocity at t=1 sec.

1/2 m/s

Find the derivative: ln(x/7)

1/x

derivative of ln(x)

1/x * x'

Derivative of loga(x)

1/xlna * x'

Derivative of arcsin(x)

1/√(1-x^2)

Find the derivative: tan^2 (5x)

10(tan5x)(sec^2 (5x))

Determine the limit algebraically, if it exists. lim(x approaches 3) (x^2 + 7x - 30)/ (x-3)

13

Find the value of the trigonometric function at the angle (-). Give an exact answer. (-) = tan^-1 (12/5) Find csc(-)

13/12

Find the derivative: x^14-(sqrt(3))

14-(sqrt(3))X^13-(sqrt(3))

Find the derivative: 4x^4 + 2x^3 + 9

16x^3 + 6x^2

Find the limit. lim(x approaches infinity) (2x + 1)/ (7x-7)

2/7

Find d/dx (x^2 - 8)

2x

Find the derivative: e^(x^2)

2xe^(x^2)

Find the derivative: (5x^4 + 1)^2

40x^3(5x^4 +1)

Write the expression (sqrt(9x^2 -16)) when 3x = 4csc(-)

4cot(-)

At time t, the position of a body moving along the s-axis is s= t^3 - 9t^2 + 24t m. Find the body's acceleration each time the velocity is zero.

6 m/s^2 and -6 m/s^2

Find the domain and range: (sqrt(3+x))

D:{-3, infinity) R:{0, infinity)

How do you find a horizontal tangent?

Find the derivative of the equation and solve for the x

Chain Rule Formula

Outside*(inside)*(derivative of the inside)

Piece wise function

a function defined by two or more equations

Derivative of a^x

a^x ln(a) * x'

Determine the values of x for which the function is differentiable. 1/(x^2 - 64)

all real numbers except -8 and 8

derivative of sinx

cosx

Simplify(csc(-)/sec(-))

cot(-)

Determine the limit algebraically, if it exists. lim(x approaches 6) (sqrt(x-9))

does not exist

Find the derivative: 3 - e^-x

e^-x

Derivative of e^x

e^x * x'

Determine if a function is even odd or neither y= 1/(x^2 + 9)

even

Find the limit when substitution doesn't work

factor out the top and bottom, cancel and then substitute

Find the limit as x approaches infinity.

find the horizontal asymptote

Quotient Rule

g(x)f'(x)-f(x)g'(x)/g(x)^2

Find the limit. lim(x approaches negative infinity) (5x^3 + 4x^2)/(x-7x^2)

infinity

when degree on top is higher than the degree on the bottom

makes a slant asymptote or a parabolic asymptote

Determine if a function is even odd or neither y= -8x^5 - 6x^3

odd

Find the limit by substitution

plug in the x-value

derivative of tanx

sec^2x

how to find horizontal asymptote

simplify the highest degree term on the top and the highest degree term on the bottom

Solve for t. (2d/t-r) = (9/t)

t=(9r/-9+2d)

Implicit Differentiation

take derivative w/ respect to x and y, solve for dy/dx

Product Rule

uv' + vu'

Find an equation for the tangent to the graph of y at the indicated point. Round to the nearest thousandth when necessary. sin^-1 (x/2), x=1

y= (1/(sqrt(3))x - (1/(sqrt(3)) + PI/6

Find the inverse of the function f(x) = 7x^3 + 3

y= (cubic root((x-3)/7))

Find the equation of the normal line to the curve y= 5x - 5x^2 at the point (-4,100)

y= -1/45x - 450/45

Given x^2 + y^2 - 2x + 4y =8, find the line that is tangent to the curve at (4,0)

y= -3/2x + 6

Write an equation for the line through P with the given conditions. Write the equation in slope-intercept form. P(2,2), parallel to L: -3x + 5y = 9

y= 3/5x + 4/5

Find an equation of the tangent line to the graph of y= x - x^2 at the point (-1,-2)

y= 3x+1

Find the numerical derivative of the given function at the indicated point. Is the function differentiable at the indicated point? f(x)= x^3 - 5x, x=-2

yes, 7