a) Find the derivative of the function using limits: f (x) = 2x+1 b) Find an equation of the tangent line to the graph of this function at the point x = 0

Q: Use the definition of the derivative to find the slope of the tangent line to the graph of the…

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Q: (1) Using the definition of derivative, find the derivative of th following functions: (a) y = xvx²…

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Q: find the derivative of y with respect to the appropriatevariable. y = ln (x2 + 4) - x tan-1 ( x/2)

A: We use the chain rule and product rule

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

A: Here the given function  hx=x+2, c=-2 The function can be written as hx=x+2,x≥-2-x-2,x≤-2

Q: Find the derivative of the function.

A: To Find the derivative of the function. y = ln sec x + tan x

Q: B. By using the definition of the derivative, find the for: - dx f(x) = x -

A: Explanation of the answer is as follows

Q: Use the definition of a derivative to find the equation of the tangent line at the given point.…

A: The equation of the tangent line is  y-7x+2=0

Q: find the derivative of y with respect to the appropriatevariable. y = tan-1√(x2 - 1) + csc-1 x, x…

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Q: find the derivative of y with respect to the appropriatevariable. y = cos-1 x - x sech-1 x

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Q: Derive the formula for the derivative with respect to x of csc x.

A: We will write cscx= 1/sinx  Then we will use the quotient rule to differentiate

Q: find the derivative of y with respect to the appropriate variable.31. y = cos-1 x - x sech-1 x…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 2х- 3 3. У3 5x +1

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Q: Find the derivative of each function at the specified value of x.

A: We have to find the derivative of the function at the given value of x: gx=ex sinπx, when x=0. We…

Q: A) Find an equation of the line tangent to the function of x + (y-x)' D9 atx 1. B) Using the…

A: Part A,Given,          The function is x2+y-x2=9 at x=1.

Q: eリ- + 2y eTy x° +

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Q: Find the derivative of the function using the definition of derivative. 1 g(x) 8 + Vx g'(x) =

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Q: find the derivative of y with respect to the appropriatevariable. y = x sin-1 x + √(1 - x2)

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Q: Find the derivative of y with respect to x. 1 y = cot 16x² - 1 + sec - 1 2 - 1 4x, 4

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Q: Use the rules of differentiation to find the derivative of the function. y = - cos(0) 8 y' =

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Q: 14. f(x) = 2 +3cos x

A: using basic properties and application of derivation we will solve this question.

Q: 3. Use implicit differentiation to find an equation of the tangent line to the curve sin(x + y) = 2x…

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Q: What is the derivative of the function with respect to x of (x + 1)³ – æ° -

A: Given : Function x+13 - x3   To find : Derivative of the given function with respect to x?

Q: Find the derivative of the function using the definition of derivative. f(x) = rx + q

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Q: y = x*(1 – In x4)

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Q: 3. Use the limit definition of the derivative to find the equation of the tangent line to the curve…

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Q: Find the derivative of the function. y = tan(4x2 + 3)

A: The given function is y=tan4x2 + 3

Q: 2. Sketch the graph of a tangent line of the function f(x) = at x = -1. And then find 1- x the…

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Q: 7. Use implicit differentiation to find an equation for the line tangent to the curve 2² + 2xy – y³…

A: Given :           x2+2xy-y3=0

Q: ■ Find the derivative of the function. Simplify wherepossible.  y =  ( tan -1 x ) 2

A: y=tan-1x2

Q: Find the derivative of y with respect to x.

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Q: 1. x² - 2xy + y² − 6x + 2 = 0

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Q: Find the derivative of the function (slope of the tangent) using the definition at the point Xo=9…

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Q: Find the derivative of the curve f(x) = 3x² - 6x + 1. Use the result to find the slope of the…

A: Follow the procedure given below.

Q: tan (2x) 3. y = sin (5x–1)

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Q: Find the derivative of y with respect to x. -1 y = tan (In(2x))

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Q: 3. Use implicit differentiation to find an equation of the tangent line to the curve 2(x + y = 25(x…

A: Explanation of the answer is as follows

Q: Find the derivative of the function. f(x) = sin (4x) %3D

A: To find the derivative of the function.fx=sin-14x

Q: 3) Use the definition of derivative (do NOT use the short cut method) to find_ƒ'(x) given that f(x)…

A: This question is based on finding slope using definition of derivative.

Q: Find the derivative of the function. f(x) 4. + 2cos x %3D

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Q: Find the derivative of the function

A: We have to find the derivatives of the function: y=x tan-12x-14ln1+4x2 If two functions are in…

Q: Find the derivative of the function using the definition of derivative. 1 f(x) V5 + x

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Q: How do you solve question 10?

A: Given function is  By definition of derivative , we have

Q: Find the equation of the line tangent to the graph of the function f(x)=x-2x^2 at x=1 use the…

A: The equation of the curve is: f(x)=x-2x2

Q: Find derivatives of f(x) = {x+- 1 and find the line tangent to it when x = 1

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Q: .If f(2) = 3 and f'(2) = 5, find an equation of the tangent line at the point where x=2.

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Q: 1. Use implicit differentiation to find the slope and equation of the tangent line given f(x) = x³…

A: Given function is  f(x) = x^3+y^3-9  According to Bartley guidelines we can attempt only one…

Q: Find the derivative using the definition 1- y = vx -1

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Q: Find the derivative of y with respect to x. 58)y tan (In 2x)

A: Firstly, we use the result that  derivative of inverse of tan of x is 1/1+x^2

Q: B) Use the definition of differentiation to find the derivative of the function f(x) = 4- Vx + 3. Is…

A: Consider the function: fx=4-x+3 The definition of derivatives is given by the formulas,

Q: Use the definition of derivative to find the tangent and normal equations of f (x) = (x – 3)2 %3D

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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: