Problem 5. In general the derivative of a product is not the product of the derivatives. Find f and g such that the derivative of fg is f'g'. Problem 6. Find the equation of the tangent line to y = e" at x = 3. Problem 7. Is it true that the slope of the tangent line to y = e" is never zero? Erplain your reasoning.

Q: What is the derivative of y = cos² x?

A: According to the chain rule of differentiation:

Q: 3. what can the derivative be used for? In essence, what are the practical applications of…

A: This is a problem related to practical application of the derivatives. Please find the procedure…

Q: Eliminate the constant/constants from the following equations. (Refer to the note)   (x-C)2 + y2 =…

A: Given x-c2 + y2 = c2To FindNeed to find differential equation taken c as arbitrary constant

Q: Discuss how the concept of instantaneous velocity v(t) can lead to the mathematical notion of a…

A: Topic:- application of derivatives

Q: Find the second derivative of y= b. -x-32 a. -3/2 4/24 C. -5/2 C. thrown vertically upward. The

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Q: Find the 42nd derivative of the function y sin(x). Give reason for choosing yours answer.

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Q: Find the slope of the tangent line to the curve y- x + 4=0 at the points (8, 2) and (8, -2) in two…

A: We will find out the required solution.

Q: y = ǀsinx ǀ Estimate and list out the values of x where derivative of this function does not exist

A: Solution:- The given function is  y=|sinx| the graph of the above function y=|sinx| is given below.…

Q: (y) = xy cos find the derivative function ot OX avis of giver Find at 30 degrees the directional…

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Q: 1. For the function f(x) = 2x2 +7x-3, %3D (a). Find the slope of the tangent line at c = 4. (b).…

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Q: Find the slope of the tangent to the curve f(x)=Jx - at (1,– 2). а. 5.5 b. 12.5 С. 13.5 d. 10.5

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Q: 1. Find the derivative of the curve given by the equation: 2(x - y) = 3+ siny

A: As per our guideline we are supposed to answer only one question you can repost other questions in…

Q: 16. Which of the following statements is true? A. The slope of a line can be applied for curves or…

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Q: Discuss two applications of derivatives to something other than tangent lines and velocities

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Q: 4. Find the slope of the tangent line to the graph f(x) = 3x² +4 at the point (2, 16) and determine…

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Q: We need to use implicit differentiation in these rates of change problems because we generally have…

A: To determine whether the following statement is true or false.We need to use implicit…

Q: Given the quadratic function in blue and the line tangent to the curve at A in red, move point A and…

A: Detailed solution is given below

Q: Problem #2: Find the derivative of 7x² - y¹⁰ = 25

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Q: Find the indicated derivative. Leave your answer in structured form. f(w) = wetan(w) f '(w)

A: We can solve this problem using chain rule of differentiation.

Q: How do I find the following derivatives?

A: Using 1 rules of log 2 derivatives of composite functions (chain rule)

Q: 1. Find the slope of the graph of the function f (x) = v3x + 4 at x = 7. Then find an equation of…

A: equation of tangent line is (y-y1) = slope (x-x1)

Q: 1. x³ V1 – x2 In x +3' 2.

A: (1).   The given function is: f(x)=x31-x2