Combinations of Functions In Exercises 35-38, find (a) f ( x ) + g ( x ) , (b) f ( x ) − g ( x ) , (c) f ( x ) ⋅ g ( x ) , (d) f ( x ) / g ( x ) , (e) f ( g ( x ) ) , and (f) g ( f ( x ) ) , if defined. See Example 5. f ( x ) = 2 x − 5 g ( x ) = 4 − 3 x
Combinations of Functions In Exercises 35-38, find (a) f ( x ) + g ( x ) , (b) f ( x ) − g ( x ) , (c) f ( x ) ⋅ g ( x ) , (d) f ( x ) / g ( x ) , (e) f ( g ( x ) ) , and (f) g ( f ( x ) ) , if defined. See Example 5. f ( x ) = 2 x − 5 g ( x ) = 4 − 3 x
Combinations of Functions In Exercises 35-38, find (a)
f
(
x
)
+
g
(
x
)
, (b)
f
(
x
)
−
g
(
x
)
, (c)
f
(
x
)
⋅
g
(
x
)
, (d)
f
(
x
)
/
g
(
x
)
, (e)
f
(
g
(
x
)
)
, and (f)
g
(
f
(
x
)
)
, if defined. See Example 5.
An elastic rope is attached to the ground at the positions shown in the picture. The rope is being pulled up along the dotted line. Assume the units are meters.
9
ground level
Assume that x is increasing at a rate of 3 meters/sec.
(a) Write as a function of x: 0=
(b) When x=10, the angle is changing at a rate of
rad/sec.
(c) Let L be the the left hand piece of rope and R the right hand piece of rope. When x=10, is the rate of change of L larger than the rate of change of R?
○ Yes
○ No
4.1 Basic Rules of Differentiation.
1. Find the derivative of each function. Write answers with positive exponents. Label your derivatives with
appropriate derivative notation.
a) y=8x-5x3 4
X
b)
y=-50 √x+11x
-5
c) p(x)=-10x²+6x3³
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.