Exploin how 가 done step by is step i :) Finding the criticol points of fonetion and clossi fying them second derivative test Vio

Q: sinx is the second derivative of what funtion? coS X h. -cos x sin x d. -sin x

A: -sinx is second derivative of what function?

Q: Find an equation of the tangent line to the curve at the given point. xy + x²y² : = 42, (6, 1)…

A: Given curve, xy+x2y2=42               ....1 And point (6, 1)

Q: Assume the derivatives of f and g exist. How do you find the derivative of the sum of two functions,…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g'(s) Need…

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Q: Suppose f(x) = 2ax° +b°x - 4c where a, b and c are real constants. Suppose that f has a horizontal…

A: Given:- Suppose f(x) = 2ax³ + b³x-4c where a, b and e are real constants. Suppose that f has a…

Q: Example: Find the derivative of each function. (a) f (æ) = (4x³ – 5æ)" - (Б) g (х) — е2^ . cot z (c)…

A: As we know that the differentiation properties:- (f(x)g(x))'=g(x)f'(x)+g'(x)f(x) Chain…

Q: "pie 33. Find the derivative of (ax + b)n by the definition of differentiation.

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Q: Part I: Find the derivative. Show all workow all 2. Y = In(sin2x)

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Q: tan(x) Which of the following is the derivative of q x e sec² (x)-e" tan(x) e2z None of the above e"…

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Q: Consider the function f(x) whose second derivative is f"(x) = 4x + 4 sin(x). If f(0) = 2 and %3D %3D…

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Q: Find the derivative of y= sec(x) tan(x) Give clear steps and explanations.

A: The given function is y=secx tanx. The following product rule is used in evaluating the given…

Q: 1 Use the fundamental theorem of calculus to find the derivative of g(x)= | dt. +1

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Q: Consider the function f(x) whose second derivative is f''(r) = 9x + 6 sin(z). If f(0) = 3 and f'(0)…

A: Given that: f''x=9x+6sinx

Q: Find an equation of the tangent line to the curve at the given point. ху+ x?у? 3D 56, (7, 1)…

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Q: AJ Find the derivative of the function: In(tan(sinx) + secx). A If v = eu 1Infs

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Q: Find the derivative. f(x) = tanh(x) f'(x) = Need Help? Read It

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Q: Find the derivative. f(x) = e* cosh(x) f'(x) = Need Help? Read It

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Q: Find an equation of the tangent line to the curve at the given point. xy + x?y? = 12, (3, 1)…

A: Equation of tangent line to the curve: Curve is :                      xy+x2y2=12 at (3,1)…

Q: Determine the derivative of the function g(x)= 2 / cosx. Do not simplify your answer.

A: Given query is to find the derivative of the expression 2cos x. Use the fact that 1cos x=sec x.

Q: a f(x) = x² sec (ax)

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Q: As a student how can you relate the topic derivative in daily life?

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Q: Define the derivative f'(a) . Discuss two ways of interpretingthis number.

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Q: Using the Limit Definition of the Derivative determine the derivative of the function below ?(?) = 5…

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Q: Question 9(both parts)

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Q: Find an equation of the tangent line to the curve at the given point. xy + x²y? = 56, (7,1) (Express…

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Q: A student incorrectly evaluated the derivative of f(x) = as f'(x) = %3D Væ + sin(x) -1/2 + cos(x)…

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Q: () Use part I of the Fundamental Theorem of Calculus to find the derivative of 17 F(x) tan F'(z)=…

A: Topic-  derivatives of definite integration

Q: Find the second derivative of the function. f(x) = sec x f"(x)= sec x sec x(sec² + tan² 2 tan²x)…

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Q: sinhz analytic or not ?

A: The given function is fz=sinhz. A function fz=ux,y+ivx,y is said to be analytic if the first partial…

Q: Use the quotient rule to find the derivative of -4 sin(2)-1 92+10 You do not need to expand out your…

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Q: Determine whether a tangent line is shown in each diagram. Type out your work/Explain 3V3 9. 3.

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Q: 5. Une differentiation rules to find the derivatives and simplify: 5.1 y - +1

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Q: Question 4

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Q: Exercise 2: Derive the formula for the derivative of arcsec(x) in two different ways: (a) Let…

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Q: 1. State two interpretations of the derivative (No formulas!). 1st: 2nd.

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Q: f(theta)=sec2(3theta)             What is the derivative of f(theta)?

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Q: Зх + 4 Calculate the derivative of f(x) 7x - 5 0. Give an exact answer in decimal form at x = f'(0)…

A: The given function is

Q: The derivative du forthe funchion 4=cot vi4-x

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. •tan(x) 3t…

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Q: Find the derivative of the function. PLEASE HELP ME ANSWER WITH SOLUTIONS    SOL 6,7

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Q: (a) Use the Second Derivative Test to find the local extreme values of the function

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Q: 236.7 derivative 0.5cos0 + 0.3515sin0

A: Why can't we use the quotient rule

Q: Find the equation of the tangent line at (2, f(2)) when f(2) = 8 and f'(2) = 3. (Use symbolic…

A: The solution is given in the next step.

Q: Find the derivative. (The Fundamental Theorem of Calculus -- Part 1) 19) y = cos ft dt COS-

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Q: HOW DO YOU FIND THE DERIVATIVE

A: In this question we have a function for which we have to find the differentiation, function is given…

Q: Explain the proof that the derivative of y=arctan(x) is This proof is in the textbook in the section…

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of sin (z) h(x): (cos (t) +…

A: Topic:- application of derivatives in integration

Q: sin (ax + b) Find the derivative of - cos (cx + d)

A: The given function is  y= [sin(ax + b)] /[cos(cx +d)] To find derivative of the function i.e. dy/dx

Q: Find an equation of the tangent line to the curve at the given point. x? (3,9) (Express numbers in…

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