The cost of producing x ounces of gold from a new gold mine is C − f (x) dollars. (a)  What is the meaning of the derivative f'(x)? What are its units? (b)  What does the statement f'(800) = 17 mean? (c)  Do you think the values of f'(x) will increase or decrease in the short term? What about the long term? Explain.

Q: what is derivative of f(x)=x/(x+1)^2

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Q: What is the derivative of ex? What does it mean that the derivative is equal to the value of the…

A: Explanation of the solution is given below...

Q: Derivative of h(x)= (x+5)^4(2x-1)^2

A: Given query is to find derivative of the expression.

Q: How do you find the fifth derivative of a function?

A: To find the derivative we differentiate the function once.  To find the second derivative we…

Q: derivative of f(x)= 1/(x^2+5) is

A: Given,          fx=1x2+5

Q: second derivative of  y=x(x-4)3

A: Given function is y = x(x – 4)^3. Differentiate with respect to x on both sides.

Q: 10) Using the First Derivative Test, what are the local extrema for the function 5(x)==x²+10 x³…

A:

Q: How do you find the derivative using the chain rule?

A: The given equation is hz=ba+z29.

Q: True or false? A function does not have a derivative at x if its left hand derivative is not equal…

A: True or false for the given statement A function does not have a derivative at x if it's left hand…

Q: Find the first derivative of f(x) = e3r

A: To find the first derivative of fx=x3e3x. Solution: Quotient rule of derivative states that:…

Q: Can you help me with this problem step by step?

A: The equation is given by

Q: first and second derivative of f(x)=x^2/(1+e^x)

A: To find first and second derivatives we will use product rule and quotient rule of derivatives. For…

Q: HOW DO YOU FIND THE DERIVATIVE

A: Given an equation of y in terms of x as shown below.Here we need to find the derivative of y with…

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: a, b, and I are differentiable functions of the same variable what is the derivative of H ac b +…

A: To find the derivative of acb, here a,b and c are differentiable function of same variable. Let a,b…

Q: Find the derivative if f(x)= ((x/2) + (x √x))ex

A: The given function is fx=x2+xxex. Obtain the derivative as follows.

Q: How do you find the derivative of the sum of two functionsƒ + g?

A: we have to determine how to determine the derivative of the sum of two functions that is f+g.

Q: How do you find the derivative of (tan(x)-4)/sec(x)?

A: Use the quotient rule to find the derivative of (tan(x) – 4)/sec(x) as follows.

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

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

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of…

A: The slope of tangent to a curve y=fx  at point a,b is given by dydxx=a.

Q: Evaluate the second derivative of the function at the given point. Use a computer algebra system to…

A: Given function is fx=1x+4. Compute the first derivative. f'x=1x+4'=-12x+432

Q: Find the derivative of f(x)=((e^x)+(x^2))(3sinx+4cosx

A:

Q: 1, Find the first and the second derivative of f(x): f(x)=x

A:

Q: Find the second derivative

A: Given, f(x)=x3x-1

Q: How do you find the derivative of f(x)= sec(x)tan(x)?

A: Some properties of derivatives:Following are some of general derivatives and derivatives of…

Q: find the derivative of the function f(x) = x2 what is f'(3)? what is the equation of the line…

A: Given function is f(x)=x2

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: Enumerate and explain the steps in finding the derivative of this function: y=1/[2*sqrt(x+3)]

A:

Q: What is the rule for calculating the derivative of a composite of two differentiable functions? How…

A: Let us we consider a function which is real valued function which is composite of of two functions…

Q: derivative of function y=\sqrt[5]{x^4} is

A:

Q: f(x)=2x^{2x}  f'(x): ? Please find first derivative

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

A: Consider the two functions f(x) and g(x). f(x)·g(x)'=f'(x)g(x)+g'(x)f(x). Here f(x)·g(x)' represents…

Q: Find the derivztive of the function

A: Topic :- derivative

Q: 32. Using one-sided derivatives, show that the function f(4) = { 3x, x>1 does not have a derivative…

A: Given: fx=x3,   x≤13x,   x>1 To Find: To show that the given function does not have a derivative…

Q: Find the absolute extrema of the function f(x) = - x* + 50x2 - 625 on the interval [- 6,6]. Find the…

A:

Q: 31. Using one-sided derivatives, show that the function f(x) = {2. [x² +x, | 3х — 2, х> 1 does not…

A: Given: fx=x2+x     , x≤13x-2   ,  x>1

Q: ³ _ x + 2y x-2y find first derivative X = to

A:

Q: How do you find the derivative of f(x)=5/1-8x using the definition of a derivative?

A: The given function is f(x)=51-8x

Q: h (x)= 3

A:

Q: How do you find the derivative of function y=x^2-2radicalx/x

A:

Q: (2+x)2, how do I find the derivative?

A: The given function is  y = f(x) = (2 +x)2

Q: Find the value of the derivative of the function f (x) = 16 - |x| at the extremum point ( 0, 16)

A: We have to find the value of derivative of the function f(x) = 16 - |x| at the extremum point…

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

A:

Q: What do you look for when you need to match the graph of a function with the graph of its…

A: Observe the behavior of graph as the value of x increases.

Q: Find the second derivative y=5e^x -2/x^3 +4sqrt(x) -12sec x + 5lnx - pi/2= Find equation of tangent…

A:

Q: Find the derivative of the function. f(x) = (2x2 − x)ln x   f'(x)=

A: