using the equation f(x)= x^2+x find slope of tangent line f′(2) using the limit definition of a derivative and the tangent line at x=4

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Q: 3. Approximate the first order derivative of f(x)= x² + 2x at x = 3, using Forward, Backward and…

A: Formulas for differences are enclosed next page

Q: 2. Implicit Differentiation Explain when you have touse implicit differentiation to find a…

A: Consider the following example xy=1

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: Differentiate both sides of the equations. Use chain rule for differentiation.

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Q: Find the derivative of the function using the definitionof derivative. State the domain of the…

A: Now

Q: Find the perpendicular distance between tangent line to the curve f(x) = ln(sin(x)) when it has a…

A: Given,f(x) = In (sin(x))To find prependicular distance between,tangent line to f(x) at slope = 3 (0…

Q: derivative of y = x^2 ln tan^2 x

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Q: x-sinx 1) lim 2) lim-(x-). tan x 3): write an equation for the tangent line at x-3 of the curve: 1…

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Q: central-difference method to approximate the derivative of f(x) = ln x² with value Use of x at 1.8,…

A: As multiple questions are there and it is not mentioned that which question to be solved, I will…

Q: Using the Limit Definition of the Derivative determine the derivative of the function below f(x)…

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Q: ing the limit definition of derivative, find the third derivative of g, given g'(x) = 2-√√x+1

A: Note that, according to Bartleby Guidelines, In the case of multiple questions, we can answer only…

Q: Determine the relative extrema using the Second derivative test. Find the point of inflection www y…

A: Let the function be, y=x(x2-5)2 Find the critical points using dydx=0 dydx=x2(x2-5)×2x+(x2-5)2…

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Q: Applications of Derivative: Tangent and Normal Line 1. For x3 + y3 = 6xy, find the point where…

A: The given equation is:x3+y3=6xyTo find the point where the tangent line is horizontal

Q: Puestion 4. Using the definition of the derivative, show that f(x) = ifferentiable at x = -3. |2x+6|…

A: we have to show

Q: 6. Using the limit defenition of the derivative, find the equation of the line tangent to the curve…

A: We have to find the slope of the tangent line at first.Then we find its equation.

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

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Q: 4. Find the derivative of f(x) = Vr +1 using the limit definition. (a) Find the slope of the tangent…

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Q: Derivative of the function is given. Identify critical values f'(x) = 5x(x-2)(x-5)^2/27

A: The given derivative of the function is given by:

Q: Which derivative rule is used to derive the Integration by Parts formula? A. The Integration by…

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Q: 2. how does differentiability and continuity determine the derivative of functions?

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Q: Using Chain Rule method Find the derivative of: 5 2. F= x³ + x² + x + 1 1. F(x) = ln Cos(x²)

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Q: 17. f(x) = x2 + x – 3

A: Answer is f'(x)= 2x+1. Explanation is given below using the limit process....

Q: 4-X

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Q: Determine the point at which the graph of the function has a horizontal tangent line. f(x) =…

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Q: Find all relative extrema and state the intervals where the function is increasing and decreasing.…

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Q: Estimate the slope of the tangent line of the function f(x)=3ex at the point x=e. slope of the…

A: Slope of the tangent line is given bythe first derivative of curve at given point.

Q: 7. Find all relative extrema. Use the Second Derivative Test to identify the local extrema. 2 f (x)…

A: Given:The given funtion is f(x)=3x+2xTo findWe have to find the relative extrema of the…

Q: derivative of  f(x) = x csc(x) - 4cos(x)

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Q: Quotient Rule for the second derivative Assuming the firstand second derivatives of f and g exist at…

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Q: Using terms like "secant line" and "tangent line", explain how evaluating f(3+ h) – f(3) lim gives…

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Q: Find the derivative of the function. f'(x) = Find f'(x) when x = 2. f'(2) = Give the slope of the…

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Q: Product Rule for the second derivative Assuming the firstand second derivatives of ƒ and g exist at…

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Q: Ln (sin? (D-C)x) Using first principle find derivative of f(x) xD-C

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Q: 7- cosh(x) 7+ cosh(x) Use appropriate rules of differentiation to find the derivative of Gx) =-

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Q: 5. Calculate the derivative of x* sin (x) showing all your work. 6. Use the limit definition of the…

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Find the derivative of the function using the definitionof derivative. State the domain of the…

A: Consider the provided function, fx=12x-13 Find the derivative of the function using the definition…

Q: Find an equation of the tangent line to the graph of y = f ( x ) at the point on the graph where x…

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Q: Equation of the line tangent to the graph of f(x)=(x)(1-2x)^3 at (-1,1).

A: The given function is: f(x)=(x)(1-2x)3 And, at point (1,-1), we have to find the equation of the…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: