Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 37E
Related questions
Question
Question 8
![1. Compute the following limits.
sin(2x)
6x
(a) lim
x →0
5√x
x+0+ sin(8√√x)
cos² (x) 1
X
(b) lim
(c) lim
x →0
cos(x²)
2. Find the derivative of 2 e*+1
x
3. Find dy by implicit differentiation for the curve e = x + y.
dx
4. Find a point on the curvey² = x²
5. Suppose f is a differentiable function and its inverse function f-¹ exists and is also differen-
tiable. Use implicit differentiation to show that
r3 - x that has a vertical tangent.
-
9. Find the derivative of
d
dx
[ƒ-¹(x)] =
=
6. Find y" for the curve cos x
sin y
7. Use implicit differentiation to find an equation of the tangent line to the curve
= 4.
y sin (2x) = x cos(2y)
at the point (1,7).
8. Use logarithmic differentiation to find the derivative of
cos² (x)
x² + x + 1
g(x)
1
ƒ'(ƒ−¹(x))*
=
X
1
y = xx.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9afd8645-a1cc-42f3-b2b8-c8f6e459bd1d%2F8c430520-3c20-4d19-9132-a1f92c6fb237%2Fbgkig33_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Compute the following limits.
sin(2x)
6x
(a) lim
x →0
5√x
x+0+ sin(8√√x)
cos² (x) 1
X
(b) lim
(c) lim
x →0
cos(x²)
2. Find the derivative of 2 e*+1
x
3. Find dy by implicit differentiation for the curve e = x + y.
dx
4. Find a point on the curvey² = x²
5. Suppose f is a differentiable function and its inverse function f-¹ exists and is also differen-
tiable. Use implicit differentiation to show that
r3 - x that has a vertical tangent.
-
9. Find the derivative of
d
dx
[ƒ-¹(x)] =
=
6. Find y" for the curve cos x
sin y
7. Use implicit differentiation to find an equation of the tangent line to the curve
= 4.
y sin (2x) = x cos(2y)
at the point (1,7).
8. Use logarithmic differentiation to find the derivative of
cos² (x)
x² + x + 1
g(x)
1
ƒ'(ƒ−¹(x))*
=
X
1
y = xx.
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