Homework Help is Here – Start Your Trial Now!
Math
Calculus
4. Prove that d - (csc (x)) = -csc (x) cot (x). dx

4. Prove that d - (csc (x)) = -csc (x) cot (x). dx

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
See similar textbooks
icon
Related questions
Question
4. Prove that d dx - (csc (x)) = −csc (x) cot (x). 5. Fill in the blank with "all", "no", or "some" to make the following statements true. Note that "some" means one or more instances, but not all. • If your answer is "all", then give a brief explanation as to why. • If your answer is "no", then give an example and a brief explanation as to why. • If your answer is "some", then give two specific examples that illustrate why your answer it not "all" or "no". Be sure to explain your two examples. An example must include either a graph or a specific function. f(x) g(x) (a) For functions f and 9, if either f(x) or g(x) is not differentiable at x = 2. (b) For is defined but not differentiable at x = 2, then functions f and g, if f and g are two functions whose second derivatives are defined, then (f g)" = f ·g" + f" ·g. (c) For functions f and g, (f(x) · g(x))' = f'(x) · g'(x). In mathematics, we consider a statement to be false if we can find any examples where the statement is not true. We refer to these examples as counterexamples. Note that a counterexample is an example for which the "if" part of the statement is true, but the "then" part of the statement is false.
Transcribed Image Text:4. Prove that d dx - (csc (x)) = −csc (x) cot (x). 5. Fill in the blank with "all", "no", or "some" to make the following statements true. Note that "some" means one or more instances, but not all. • If your answer is "all", then give a brief explanation as to why. • If your answer is "no", then give an example and a brief explanation as to why. • If your answer is "some", then give two specific examples that illustrate why your answer it not "all" or "no". Be sure to explain your two examples. An example must include either a graph or a specific function. f(x) g(x) (a) For functions f and 9, if either f(x) or g(x) is not differentiable at x = 2. (b) For is defined but not differentiable at x = 2, then functions f and g, if f and g are two functions whose second derivatives are defined, then (f g)" = f ·g" + f" ·g. (c) For functions f and g, (f(x) · g(x))' = f'(x) · g'(x). In mathematics, we consider a statement to be false if we can find any examples where the statement is not true. We refer to these examples as counterexamples. Note that a counterexample is an example for which the "if" part of the statement is true, but the "then" part of the statement is false.
Expert Solution
Step 1

As per the company's guidelines, we are supposed to solve first question for you, kindly repost other question as a next question.

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS