What is the rule for calculating the derivative of a composite of two differentiable functions? How is such a derivative evaluated?

Q: Explain how the first derivative of a function determines where the function is increasing and…

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Q: 1/x using the definition o

A: we have to find the derivative of f(x) using the first principal. f(x)=x+1x

Q: Determine the derivative of f(x) = Cosh(5 x) csc(x)

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Q: Find the derivative of the function using the definition of derivative.

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Q: How is this derivative found?

A: Given expression

Q: Use the limit definition of derivative to find the derivative of the function with respect to x.…

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Q: How can you sometimes graph the derivative of a function when all you have is a table of the…

A: We can draw the graph of derivative of a function using the values given to us in table of of the…

Q: 2. If the derivative of an accurately determined function is replaced with a finite difference, how…

A: Since you have asked multiple question, we will solve first one for you. If you want other question…

Q: Define the second derivative of f. If f(t) is the position  function of a particle, how can you…

A: Second derivative is derivative of the derivative.      Therefore,…

Q: What is the First Derivative Test for Local Extreme Values? Give examples of how it is applied.

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Q: Use the graph of the function to sketch the graph of the derivative. (on the same grid is fine)

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Q: State the Second Derivative Test

A: Second Derivative Test:   This is used to find local extrema.

Q: How do you find the derivative of a constant multiplied by afunction?

A: If f(x) is any function and let y=cf(x)            function f(x) multiplyed with a constant, c is…

Q: What is the derivative of the following function

A: Given that: 1. h(y)=y1-ey2. f(t)=1+5tln(t)

Q: Explain what happens when the derivative of a differentiable function is zero ?

A: To explain when a derivative of differentiable function is zero.

Q: Match the graph of the function with the graph of its derivative.

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Q: Use the First Derivative Test to find the relative extrema of x – 3 f(x) ex

A: The given function is fx=x-3ex. We need to find the realtive extrema. Concept used:  Consider x=c is…

Q: Find the relative extrema using first derivative test   f(x)=(x-2)^6

A: Consider the function f(x)=(x-2)^6

Q: What is the derivative of f(x) g(x) in terms of f and g? Compute the derivative of -sin(x) · 2x=1…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Describe the Second Derivative Test in your own words

A: A second derivative test is conducted to find the relative maxima and  minima of a given function.

Q: Calculate the derivative using the appropriate rule or combination of rules. f(x) = (x + 4)(x + 2)(x…

A: The derivative of the given function is solved below.

Q: 8 Use the power rule to find the derivative of f(x) = x°. f'(x) =

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Q: Find the derivative of the function using the definition of derivative. f(x) = x4 f'(x) = %3D

A: To find the derivative of the given function using the definition of derivative.

Q: What is sign analysis of first derivative?. When a function is said to be increasing, decreasing…

A: As per our guidelines, I have solved the fourth problem. If you want the answer of the fifth…

Q: Explain the relationship between the slope and the derivative of ƒ(x) at x = a.

A: Given function is  fx at x=a

Q: Use definition of derivative to find derivative of the function f(x)=3/x+2, at x=-1

A: Given f(x)=3x+2    at x=-1To find f'(x) at x=-1

Q: What is a derivative?

A: The derivative of a function can be defined in two ways, one approach is graphical and other…

Q: 4

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Q: Determine the anti derivative of the function please

A: Here given function as fx=3ex+11-x2-2sec2x-71+x2

Q: Determine the derivative of the given function by using two different methods

A: Given,         y=x2-3x2+34

Q: How do you use the second derivative test to analyze concavity of a function?

A: We know that, If the second derivative of the function f(x) is defined on an interval (a,b) and…

Q: Find the derivative of the algebraic functions f(x) = x (1-) x+3, : g(x) = x + cotx

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Q: How do you find the derivative of the quotient of two functionsthat are differentiable at a point?

A: Given: Let f and g be two differentiable function at point x.

Q: Estimate the derivative of the function f (x) = - 3 at the point x = 3. 5 5

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Q: Find the derivative and simplify: f(x)=ex-cotx

A: To determine the derivative.

Q: derivative

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Q: What is the inverse process of determining a function whose derivative is known?

A: The inverse process of determining a function whose derivative is known is called

Q: State the First Derivative Test.

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Q: When given a function f(x), describe (in common language) what the derivative function f'(x) is and…

A: Solution 1:   The derivative of a function f(x) of a variable x is a measure of the rate at which…

Q: The Definition of Derivative

A: Question is solved.

Q: h (x)= 3

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Q: State the second-derivative test for functions of two variables.

A: State the second - derivative test for functions of two variable.

Q: Find the derivative of f(x) at the designated value of x (Using Derivative Rules). 3 11. f(x) = x*,…

A: Given :   f(x)=x4 , at x=3/2 f(x)=1/4 , at x=2

Q: State the notation/symbol for: derivative of y with respect to x derivative of f(x) second…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Find the derivative of the given function by using definition of derivative  f(x)= sec(x)

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Q: How do you find the derivative of the quotient of two functions that are differentiable at a point?

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Q: What is the definition of the derivative (Difference Quotient)?

A: 2. What is the definition of the derivative(difference quotient)? ans. In single-variable calculus,…