2. Use the product rule (and maybe the chain rule) to find the derivatives of the following functions. 4. Find the derivatives of the following functions. a) y = x sin(x) b) g = tet x3 a) y c) h(y) = e cos (y) (x+3)5 b) g = (t+1) √t − 1 d) s(t) = 3t ln (t) e) f(x)=sin(x) In (x) f) u (z) = e² (z² + 1) c) h(y)= = 2y - 1 √y +1 d) s(t): 420 (t+ 2)² (3t4t5) 42 (8 − t)¹ 8 g) y = (3 — 4x²)x−1/2 h) y = (1 + sin (0)) (1 − sin (0)) 3 x2 -5 e) f(x) = i) g(z) = √√zln (z) j) f(x) = e²+1 (2x+1) 2.3 - x f) u (z) = 3z4 5z+2 k) A = cos (5s) sin (3s) 1) a(t) = t² In (t²) g) y = cos (5 sin (2)) h) y = 4 sin (√√1 + √ē) m) h(x) = (x² + 3x) (ex − 1) (√x − 3x) o) y = (t + 1) (√√t² − 1) ¹ 1 i) g(z) = = n) p(s) = (e3x+5) In (cos (s))² p) f (0) = csc (0) tan (0) cot (0) sin (0) 5. If you really want to practice your algebra, find the second derivative of all the problems on this worksheet. 1+ cos² (7x) j) f(x) x3+1 3. Use the quotient rule to find the derivatives of the following functions. x+1 a) y = x-1 sin (t) b) g = t c) h(y): e) f(x) = sin (y) t²+1 d) s(t): = еу t +1 cos (x) In (z) f) u (z) √x z g) y = Ꮖ COS (x i) g(z) = 1 z2 √z h) y = j) f(x) 0+ sin (0) cos (0) = x23x1 2 3 d Chain Rule: · (ƒ (g(x))) = ƒ′ (g(x)) · g′ (x) dx d Product Rule: | (f(x)g(x)) = f'(x)g(x) + f(x)g'(x) dx Quotient Rule: d dx (f(x)) = f'(x)9(x) = f(x)9′(x) 1. Use the chain rule to find the derivatives of the following functions. a) y = √√√5-x c) h(y) = (1+2y) 4 e) f(x) = cos(x) g) y = ln (sin (x)) i) g(z) = √ln (x) k) A = (csc (s) + cot (s))-1 m) h(x) = sin² (3x) o) y = sin³ (3 + 4) b) g = 3/2t-t² d) s(t) = (3 — 2t²)-5 f) u (z) = sin (3z² - 2z+1) h) y = tan³ (0) j) f(x) sin (5x) cos (2x) 1) a(t) = (sin (t) + cos (t))5 n) p(s): = In (cos (s))² p) f (0) = sin (√) 1
2. Use the product rule (and maybe the chain rule) to find the derivatives of the following functions. 4. Find the derivatives of the following functions. a) y = x sin(x) b) g = tet x3 a) y c) h(y) = e cos (y) (x+3)5 b) g = (t+1) √t − 1 d) s(t) = 3t ln (t) e) f(x)=sin(x) In (x) f) u (z) = e² (z² + 1) c) h(y)= = 2y - 1 √y +1 d) s(t): 420 (t+ 2)² (3t4t5) 42 (8 − t)¹ 8 g) y = (3 — 4x²)x−1/2 h) y = (1 + sin (0)) (1 − sin (0)) 3 x2 -5 e) f(x) = i) g(z) = √√zln (z) j) f(x) = e²+1 (2x+1) 2.3 - x f) u (z) = 3z4 5z+2 k) A = cos (5s) sin (3s) 1) a(t) = t² In (t²) g) y = cos (5 sin (2)) h) y = 4 sin (√√1 + √ē) m) h(x) = (x² + 3x) (ex − 1) (√x − 3x) o) y = (t + 1) (√√t² − 1) ¹ 1 i) g(z) = = n) p(s) = (e3x+5) In (cos (s))² p) f (0) = csc (0) tan (0) cot (0) sin (0) 5. If you really want to practice your algebra, find the second derivative of all the problems on this worksheet. 1+ cos² (7x) j) f(x) x3+1 3. Use the quotient rule to find the derivatives of the following functions. x+1 a) y = x-1 sin (t) b) g = t c) h(y): e) f(x) = sin (y) t²+1 d) s(t): = еу t +1 cos (x) In (z) f) u (z) √x z g) y = Ꮖ COS (x i) g(z) = 1 z2 √z h) y = j) f(x) 0+ sin (0) cos (0) = x23x1 2 3 d Chain Rule: · (ƒ (g(x))) = ƒ′ (g(x)) · g′ (x) dx d Product Rule: | (f(x)g(x)) = f'(x)g(x) + f(x)g'(x) dx Quotient Rule: d dx (f(x)) = f'(x)9(x) = f(x)9′(x) 1. Use the chain rule to find the derivatives of the following functions. a) y = √√√5-x c) h(y) = (1+2y) 4 e) f(x) = cos(x) g) y = ln (sin (x)) i) g(z) = √ln (x) k) A = (csc (s) + cot (s))-1 m) h(x) = sin² (3x) o) y = sin³ (3 + 4) b) g = 3/2t-t² d) s(t) = (3 — 2t²)-5 f) u (z) = sin (3z² - 2z+1) h) y = tan³ (0) j) f(x) sin (5x) cos (2x) 1) a(t) = (sin (t) + cos (t))5 n) p(s): = In (cos (s))² p) f (0) = sin (√) 1
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:2. Use the product rule (and maybe the chain rule) to find the derivatives of the following functions.
4. Find the derivatives of the following functions.
a) y = x sin(x)
b) g = tet
x3
a) y
c) h(y) = e cos (y)
(x+3)5
b) g = (t+1) √t − 1
d) s(t) = 3t ln (t)
e) f(x)=sin(x) In (x)
f) u (z) = e² (z² + 1)
c) h(y)=
=
2y - 1
√y +1
d) s(t):
420
(t+ 2)² (3t4t5) 42
(8 − t)¹ 8
g) y = (3 — 4x²)x−1/2
h) y =
(1 + sin (0)) (1 − sin (0))
3
x2
-5
e) f(x) =
i) g(z) = √√zln (z)
j) f(x) = e²+1 (2x+1)
2.3
- x
f) u (z) =
3z4
5z+2
k) A = cos (5s) sin (3s)
1) a(t) = t² In (t²)
g) y = cos (5 sin
(2))
h) y = 4 sin (√√1 + √ē)
m) h(x) = (x² + 3x) (ex − 1) (√x − 3x)
o) y = (t + 1) (√√t² − 1) ¹
1
i) g(z) =
=
n) p(s) = (e3x+5) In (cos (s))²
p) f (0) = csc (0) tan (0) cot (0) sin (0)
5. If you really want to practice your algebra, find the second derivative of all the problems on this
worksheet.
1+ cos² (7x)
j) f(x)
x3+1
3. Use the quotient rule to find the derivatives of the following functions.
x+1
a) y =
x-1
sin (t)
b) g =
t
c) h(y):
e) f(x)
=
sin (y)
t²+1
d) s(t):
=
еу
t +1
cos (x)
In (z)
f) u (z)
√x
z
g) y =
Ꮖ
COS (x
i) g(z)
=
1
z2
√z
h) y =
j) f(x)
0+ sin (0)
cos (0)
=
x23x1
2
3
Transcribed Image Text:d
Chain Rule:
· (ƒ (g(x))) = ƒ′ (g(x)) · g′ (x)
dx
d
Product Rule:
| (f(x)g(x)) = f'(x)g(x) + f(x)g'(x)
dx
Quotient Rule:
d
dx
(f(x)) = f'(x)9(x) = f(x)9′(x)
1. Use the chain rule to find the derivatives of the following functions.
a) y = √√√5-x
c) h(y) = (1+2y) 4
e) f(x) = cos(x)
g) y = ln (sin (x))
i) g(z) = √ln (x)
k) A = (csc (s) + cot (s))-1
m) h(x) = sin² (3x)
o) y = sin³ (3 + 4)
b) g = 3/2t-t²
d) s(t) = (3 — 2t²)-5
f) u (z) = sin (3z² - 2z+1)
h) y = tan³ (0)
j) f(x)
sin (5x)
cos (2x)
1) a(t) = (sin (t) + cos (t))5
n) p(s): = In (cos (s))²
p) f (0) =
sin (√)
1
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