Question

1. Use the product rule for differentiation to find derivatives in each of the following:

(a) ?(?)=(2?^{3}+4?^{2}−1)(3?^{2}−5?−2)
(b) ?(?)=(2?^{4}+1)(3√?−2)

(c) ?(?)=(3?−1)(6/?+4?−1)

Answer #1

2. Use the product rule for differentiation to find derivatives
in each of the following:
(a) ?(?)=(?2−4?−2)(?3+3?2−1)
(b) ?(?)=(2?2−1)(√?+2)
(c) ?(?)=(2/?2−3/?+2?)(3?−1)

1). Use the techniques of differentiation to find the
derivatives of the following functions
a). f(x)= (2 sqrt x + 1) (2-x/x^2+3x)
b). f(x)= cos^2 (3 sqrt x)
c). f(x) = Sin x/(x^2 + sin x)

Calculate derivatives for the following, Use proper
notation.
a) y=3x^5+4x+6
b) ?(?)=3√? + 5 ?3
c) ? = ?4ln(?) (product rule)
d) ?(?) = √4?2 + 1 (chain rule)

1. Find the derivatives of each of the following functions:
(a) ?(?)=5?3−7?2−9?+√5 (b)
?(?)=3?-4+6√?
(c) ?(?)=6/?4−7/?3+3/?+1

Use the Chain Rule to find the indicated partial derivatives. ?
= ?^ 2 + ?^ 2 , ? = ?? cos ? , ? = ?? sin ?
??/??, ??/?? , ??/?? ?ℎ?? ? = 2, ? = 3, ? = 0°

Regarding Product Differentiation:
1.Define product differentiation.
• 2.Explain horizontal vs. vertical product differentiation.
• 3.How can advertising act as a barrier to entry?.
• 4.Explain search vs. experience goods in advertising. .
• 5.Define advertising intensity.
• 6.Know the Dorfman-Steiner condition for an optimal
price-advertising strategy, and be able to apply given values for
the formula.

Consider the surface x^7z^2+sin(y^7z^2)+10=0
Use implicit differentiation to find the following partial
derivatives.
∂z/∂x=
∂z/∂y=

Use the Chain Rule to find the indicated partial
derivatives.
N =
p + q
p + r
, p = u + vw, q =
v + uw, r = w + uv;
∂N
∂u
,
∂N
∂v
,
∂N
∂w
when u = 6, v = 5, w = 7

Using Leibniz notation (i.e., ??/??, ??/??, etc.), find
derivatives for each of the following functions. You should always
use proper notation. Your answers must be simplified.
a) ?=(3√p/(p√p))^−2
b) ?(?)=cos?/(5?^? +2tan(?))
c) ?=sin^−1((sqrt?+1))
d) ℎ(?)=?^2?^(?3)
e) ?(?)=cot^−1(?)+cot^(−1)(1/?)

Use the Chain Rule to find the indicated partial
derivatives.
w = xy + yz + zx, x = r
cos(θ), y = r
sin(θ), z = rθ;
∂w
∂r
,
∂w
∂θ
when r = 4, θ =
π
2
∂w
∂r
=
∂w
∂θ
=

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