Question

**1). Find the derivative of the function**

f(x) = ln(x9 + 3) − 4ex/2 − x

.

**2). Find the equation for the tangent line to the curve
y = f(x) at the given x-value.**

f(x) = x ln(x − 5) at x = 6

.

**3). Use implicit differentiation to find
dy/dx.**

y^{2} − ye^{x} = 19

.

**4). The United States population (in millions) is
predicted to be P(t) =
317e^{0.01t}, where
t is the number of years after 2013.† Find the
instantaneous rate of change of the population in the year 2050.
(Round your answer to two decimal places.)**

.

**5). Election returns are broadcast in a town of 1
million people, and the number of people who have heard the news
within t hours is 1,000,000(1 −
e^{−0.6t}). How long
will it take for 750,000 people to hear the news? (Round your
answer to two decimal places.)**

Answer #1

Find the derivative of f(x) = 3^(x ln x) and f(x) = ln( 1/ x ) +
1/ ln x

Part 1) Find the derivative of the function
f(x)=e^((x^2)/(x^2+4))
Part 2) Find the derivative of the function
f(t)=(e(^t^2)+4t)^4
Part 3) Find the derivative of the function y=log6sqrt(8x+3)
Part 4)
The number x of stereo speakers a retail chain is willing to
sell per week at a price of pp dollars is given by
x=78sqrt(p+24) -390
Find the supply and instantaneous rate of change of supply when
the price is 75 dollars.
Supply = 386
Instantaneous rate of change of supply...

Find the derivative of the function.
(a) f(x) = ln (x) + 6x^(2) – 5
(b) f(x) = ln (x + 1)
(c) f(x) = 5 ln x
(d) f(x) = ln(x^(3) – 5x^(2) – 2x + 5)
(e) 2lnx / x
(f) x^(2) ln x

Use implicit differentiation to find dy dx for x^2 y^3 + 3y^2 −
5x = −10.
(b) Find the equation of the line tangent to the curve in part
a) at the point (1, 2).

Use Implicit Differentiation to find first dy/dx , then the
equation of the tangent line to the curve x2+xy+y2= 2-y at the
point (0,-2)
b. Determine a function of the form f(x)= ax2+ bx + c (that is,
find the real numbers a,b,c ) if the graph of the function has
slope 2 at the point (3,4) , and has a horizontal tangent where
x=1
c. Assume that x,y are functions of variable t satisfying the
equation x2+xy=10. Find dy/dt...

3. Consider the equation:
x^2y −√y = 2 + 4x^2
a) Find dy/dx using implicit differentiation. b)Construct the
equation of the tangent line to the graph of this equation at the
point (1, 9)

13. Consider
f(x)=sqrt x-2
a) Using any of the three limit formulas to find f ′ ( a
), what is the slope of the tangent line to f ( x )at x = 18? (6
points execution, 2 points notation)
b) Find the equation of the tangent line at x =
18
14. State the derivative.
a) d/ d x [ x ^n ]
b) d /d x [ cos x ]
c) d /d x [ csc...

Consider x^2 +sin(y)=4xy^2 +1
a.)Use Implicit differentiation to find dy/dx
b.) find an equation tangent of the line to the curve x^2
+sin(y)=4xy^2 +1 at (1,0)

Find the directional derivative of the function
f(x,y,z)=ln(x2+y2−1)+y+6z at the point (1,1,0) in the direction of
the vector v→=i→−2j→+2k→

Find the directional derivative of the function
f(x,y,z)=ln(x2+y2−1)+y+6z at the point (1,1,0) in the direction of
the vector v→=i→−2j→+2k→.

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