6. Using the limit defenition of the derivative, find the equation of the line tangent to the curve f (x) = x2 - 3 at the point where x = 2 %3D %3D

Q: Find the derivative of the function by the limit process.

A: We have to find derivative of the function using limit process: fx=x+4 We know the formula of…

Q: Find the equation of the tangent line to the graph of y at (2, 금). Use the limit process in finding…

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Q: Find the derivative of the function by the limit process. f(x) = 1/(x − 1)

A: We use the limit definition of the derivative

Q: 4. Calculate the derivative of the given function directly from the definition of derivative y = v2x…

A: Given function is  y=√(2x+1)

Q: If f(x)=4/x, find the derivative of f(x) at x=2 using the limit definition of the derivative at a…

A: given function f(x)=4/x we have to find a) the the derivative of f(x) at x=2 using the limit…

Q: 4. Find an equation of the tangent line to the curve, f(x) definition of the derivative. (Don't use…

A: Given problem:- Find an equation of the tangent line to the curve, f(x) = 1/(x2 + 1) by using the…

Q: find the derivative of y with respect to the appropriatevariable. y = csch-1 (1/2)θ

A:

Q: Find the derivative of the function by the limit process. f(x) = √(x + 4)

A: Given function is

Q: eリ- + 2y eTy x° +

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Q: find the derivative of y with respect to the appropriatevariable. y = √(s2 - 1) - sec-1 s

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Q: 1 Find the first derivative given that f(x) = xdx +

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Q: 2. Find the first derivative given that f(x)=x√√x + 1 x²√x

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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 by the limit process. h(s) = −2 (square root of x)

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Q: 2. Find the derivative of y= ecos{/x+3) Solution:

A: Topic:- derivatives Note:- as per our guideline if more than one question uploaded than only first…

Q: find the derivative of y with respect to the appropriatevariable. y = (sech θ)(1 - ln sechθ)

A: We have to take derivative with respect to θ. dydθ=sinh θ ddθ1-ln sech θ+1-ln sech θddθsinh θ

Q: 8. Find the derivative of the function. y= In(1+x)

A:

Q: Find the tangent line to the curve y = x^2 −5x + 11 at the point (1, 7). Use the limit definition of…

A: slope of the tangent line is m=dydx at (1,7)   By limit definition of…

Q: find the derivative of y with respect to the appropriatevariable. = cosh-1 2√x + 1

A: Given: y=cosh-12x+1Here ,we havecoshy=2x+1Taking the derivatives on both…

Q: 1) Find the derivative of the function 2 + X y = arctan V 2 – x .Simplify where possible.

A: Answer and explanation is given below..

Q: 1 at x= 4 by using the 2Vx Q2. Find the slope of the tangent line to the function f(x)= definition…

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Q: 5. First compute the derivative of f(x)= Vĩ and then use it to: a. Find the equation of the tangent…

A: Given equation of curve is fx=x. Power rule of differentiation states that: ddxxn=nxn-1…

Q: 3) Find the derivative of the function f(x)= x² –x+2 using the definition of the derivative (a…

A: Given:     To determine: Derivative of the function using the definition of the derivative.

Q: 6. Sketch the graph of y= x2+ by using the properties of the derivative.

A: The given function y=x2+2x

Q: 4. Find an equation of the tangent line to the curve, f(x) = definition of the derivative. (Don't…

A: On solving this we will get

Q: find the derivative of y with respect to the appropriatevariable. y = (x2 + 1) sech (ln x)

A: Given: y=x2+1sechlnx

Q: 1. Use the limit definition of the derivative to determine the derivative.2. Determine the equation…

A: We have to find derivative using limit definition of derivative and then find tangent line to f(x)…

Q: find the derivative of y with respect to the appropriatevariable. y = csc-1 (x2 + 1), x > 0

A: Given that, y=csc-1x2+1

Q: Suppose the derivative of ƒ is ƒ'(x) = x - 3.a. Find the critical points of ƒ.b. On what intervals…

A: We have to find: a. critical points of fb. On what intervals is f increasing and on what intervals…

Q: find the derivative of y with respect to the appropriatevariable. y = (θ2 + 2θ) tanh-1 (θ + 1)

A: The given function is y=θ2+2θ tanh-1θ+1. Obtain the derivative as follows.

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = 1/ln 3x

A: Given:

Q: 2. Prove from the definition of derivative that for n EZ, d ng"-1 dr

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Q: find the derivative of y with respect to the appropriatevariable. y = sec-1 (2s + 1)

A: The given function is y=sec-12s+1.

Q: Find the equation of the tangent line to the function f(x) = x² – 2 at the point (1,-1). You must e…

A: Given, fx = x4 -2  We have to find the equation of the tangent line to function at the point 1, -1.

Q: 2. If f (x) = xV x + 3, find the derivative of this function and the slope of the tangent line at…

A: Product rule of differentiation: (fg)'=fg'+gf' The slope of a tangent line at (a,b) is given by:…

Q: Use forward-difference formula to evaluate the first derivative of y = tan(x) at x = 4 using a value…

A: Given function is y=tanx. We have to find the first derivative of y=tanx at x=π4 using a value of…

Q: 2. Find from first principle the derivative with respect to x of the function f(x)= Inx.

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Q: How do you solve question 10?

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

Q: Let f(x) : 3x Using the limit definition of the derivative, find the equation x +1 of the line…

A: Given data: The given function is f(x)=3x/(x+1). The given point is (a, b)=(2, 2). The expression…

Q: find the derivative of y with respect to the appropriatevariable. y = csch-1 2θ

A: Given, y=csch-12θ

Q: 2. Find the derivative In (x+) y3=

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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: 3. Find the derivative of y with respect to the appropriate variable. x y= 6sinh :

A: Solution: y=6sinhx3

Q: Consider the function f(x) = x³ Q 2: Calculate its first derivative at point x = 3 numerically with…

A: We have given , f(x) = x3

Q: find the derivative of y with respect to the appropriatevariable. y = csc-1 x/2

A: We have to find derivative of y with respect to the appropriate variable: y=cosec-1x2 Rewriting the…

Q: 8) Using your derivative from the previous question, determine the equation of the tangent line at…

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Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln 3x + x

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Q: 1. Use the definition of the derivative to find the derivative of f(x)- V-x-2

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Q: find the derivative of y with respect to the givenindependent variable. y = 3-x

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