Question

#1: Consider the following.

**g(x) = 9x ^{2} − 8; h(x) =
1.1^{x}**

Find the derivative of f(x) = g(x) · h(x)

f '(x) =

#2: Consider the following.

**g(x) = 2e ^{6.5x}; h(x) =
2(6.5^{x})**

Find the derivative for f(x) = g(x) · h(x)

f '(x) =

#3: Consider the following.

**g(x) = 8e ^{−x} + ln x; h(x) =
9x^{2.7}**

Find the derivative for f(x) = g(x) · h(x)

f '(x) =

Answer #1

Consider the following functions
f(x) =x^2, g(x) = lnx, h(x) = cosx
For each of the following parts, you may use compositions,
products, and sums of thefunctions above, but no others. For
example, we can combine in the following waysh(g(x)) = cos(lnx), or
g(x)h(x) = lnxcosx, or g(x) +h(x) = lnx+ cosx
show how derivative rules apply to the function you came up
within order to produce the requested derivative.
1)A functionk(x) whose derivative is k′(x) = −tanx=
-(sinx/cosx)
2)...

[2 marks] Find the derivative of y =
√
4 sin x + 6
at x = 0.
Consider the following statements. The limit
lim
x→0
g(4 + h) − g(4)
h
is equivalent to:
(i) The derivative of g(x) at x =
h
(ii) The derivative of g(x + 4) at x
= 0
(iii) The derivative of g(−x) at x
= −4
Determine which of the above statements are True (1) or False
(2).
If f (3) = ...

Find the derivative of the following functions
(a) f(x) = ln(√x3 −2x)
(b) g(x) =√x2 + 3 x3 −5x + 1
.

find the derivative using a definition of the derivative (h) of the
following function
f(x)= x/(x-1)

1. Find the derivative of the function.
y = e−8/x
2. Find the derivative of the function.
s = t8et
3. Find the derivative
of the function.
y = ex5 − (ex)5
4. Find the derivative of the function.
y = e−5x ln(6x)

1020) y=8/sqrt(4x^7)=Ax^B + C. y'=Kx^F + G. y'(9)=H. Find A,B,C,K,F,G,H. ans:7
1026) Find the derivative of y=(5x^(1/4) - 8x^(1/7))^3, when x=2. ans:1
1010) y=3x^2 + 2x + 5 and y'=Ax^2 + Bx + C. Find A,B,C. Next Question:
y=(x^2)/7 + x/4 + 2 and y'=Hx^2 + Fx + G. Find H,F,G. ans:6

Find the derivative of the given expression.
f(x)=17x^2+ln(x^3)
f'(x)=
Solve the following equation for x:
ln(x−4)+ln(x−2)=ln(8)ln(x−4)+ln(x−2)=ln(8)
If more than one solution exists, separate your answers with a
comma.

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

Consider f(x) = x2 – 8x. Find its derivative using
the limit definition of the derivative. Simplify all
steps.
a. Find f(x + h).
____________
b. Find f(x + h) – f(x).
____________
c. Find [f(x + h) – f(x)] ÷ h.
____________
d. Find lim (hà0) [f(x + h) – f(x)] ÷ h.
____________
e. Find an equation of the line tangent to
the graph of y = x2 – 8x where x = -3. Present your
answer...

1. Find the derivative of
f(x)= √4-sin(x)/3-cos(x)
2. Find the derivative of
1/(x^2-sec(8x^2-8))^2

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