I. Use the definition of the derivative f'(x) = lim 7&+h)=Jx) to find the derivative of the following functions. Show your step by step solution. h→0 JOHN HNC GIL

Q: Apply the Chain Rule to find the tangent line to f(x) = 4/2x – 6e²-*at x = 2

A: The given problem is to find the tangent line to the given function at given point x=2 Given…

Q: Suppose that f(x) is differentiable for x > 0, y = 2x + 1 is the tangent line to the graph of f at x…

A:

Q: Section 2.4 Chain Rule Please show & explain all work, thank you.

A: Multiply both sides by x^2.

Q: 3. Determine the slope of the tangent line to the curve f(x) = at (2x + 1)2 x = 1 by using the…

A:

Q: Use backward, forward, and centered difference approximation to estimate the second derivative of…

A: We will do all three parts.

Q: Find the equation for the tangent to the curve at the given point using the limit definition of…

A: Find the equation for the tangent line to the curve at the given point by using the limit definition…

Q: Find the slope of the line tangent to the curve x - 3xy + 4x = 2 at x = 1. -5/3 O 2/3 O 1/3 O 4/3

A: The given curve is: x3-3xy+4x=2 We need to find the slope of the line tangent to the given curve.…

Q: Evaluate the derivative at x = 1 for y = In ()

A: For a function f its derivative is defined as f'(x)=limh→0f(x+h)-f(x)h. For some standard functions…

Q: calculate the derivative with respect to x. xey = 2xy + y3

A:

Q: . Find the derivative with respect to x: y = tan¬(Vx² –- 1) + csc¯²(x),x > 1

A: Given thaty=arctanx2-1+arccscx To find its derivative

Q: Find the derivative of the follourng funchion y=x sin'x %3D

A: We have to find the derivative of the given function   The given function is y=x sin-1x3it can…

Q: Find the derivative of y with respect to X, t, or 0, as appropriate. Inx y=5

A: Given: y=ln xx5 So, the derivative of y with respect to x is: dydx=ddxln xx5 According to the…

Q: Find the equation of the tangent line to f(x) =1 – x² at (1,0). -

A: here we use formula  y-y1=m(x-x1) at point (1,0)

Q: Find the equation of the tangent line to the function f(x) = -3x2 – 2x at the point where x form y =…

A:

Q: Find the equation of the tangent line of f(x) = 8/x+3 at the point (4, 19) . Express your answer in…

A: Find the equation of the tangent line of fx=8x+3 at the pint (4,19).

Q: ) Find the equation of the tangent line ETL for f(x) = x³ - 2x +1 at x = −1

A:

Q: 2. Use the definition of the derivative to find f'(x) and f"(x). a) f(x) = x? %3D

A:

Q: Find an equation of the tangent line to f(x) = x² at the point (3,9).

A:

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

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Q: Use three-point midpoint formula to evaluate the first derivative of y=tan(x) at x = O-2√/2 00…

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

Q: or x>0, determine the deriva

A: Consider the given function: Here the objective is to find the derivative of a given function using…

Q: Find the derivative with respect to x: y = tan(Vx2 – 1) + csc-(x),x > 1

A:

Q: Find an equation of the tangent line to f(x) = x° – 2x +1 at the point (0, 1).

A: The given function is: f(x)=x3-2x+1

Q: Find f(x) if f(1) = -1 and the tangent line at (x, f(x)) has slope 3ex+7 f(x)= ?

A: Given:

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. Inx y = x7

A:

Q: Let ƒ(x) = √2x + 1. Compute ƒ'(2),the derivative of ƒ at x = 2, and use the result to find an…

A: Consider the given function, fx=2x+1 differentiate with respect to x, f'x=ddx2x+1=122x+1·2=12x+1…

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y= In(In 9x)

A: The solution for the above question is as shown below.

Q: Find the equation of the tangent line to the graph of the function f (x) = 4xcosx + 3 at the point…

A: Given that: f(x)=4x.cosx+3 at point (0, 3)

Q: f(x) = @tann + In (sec x) - ex at x = T

A: We know that general formula of derivatives is -  d(lnx)/dx = 1/x ; d(tanx)/dx= sec2x d(secx)/dx =…

Q: Find the slope of the tangent line on the curve y = x3 - 2x2 – x at x = -2. -6 O -19 O 19 O 6

A:

Q: Find the slope of the line tangent to f(x) = tan x at x=-. 4

A:

Q: Find the equation of the tangent line to the function f(x)=-3x^2-2x at the point where x=1. Give…

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 67) y = In 8x2

A: Since the expression contains x, we have to find derivative with respect to x.

Q: Find the equation of the tangent line on the curve f(x) = V5x + 6 at x = 2.

A: Proceed as shown below...

Q: Find the equation of the tangent line to the function f(x)=2x2-x  at the point where x=−1. Give your…

A:

Q: 4. Find the tangent line to the function f(x) =;xVx² + 5 at the point (2,2).

A: Tangent line of a function:  Differentiate the equation of the curve Substitute the value into the…

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(r) =…

A: The limit definition of the derivative is

Q: f(x) = ln(x − 1) at x = 2

A:

Q: .. Consider the quadratic function y = 4-x². Using the limit definition, ind the derivative of the…

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Q: Find the equation of the tangent line to the graph of f(x)= x ln(2x+3) at the point (-1,0).

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Q: Find the equation of the tangent line to the curve f(x)= Va. Assume f'( x) 1 at x = 4.

A:

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

A:

Q: 8. y = va? + x²

A:

Q: Find the equation of the tangent line to the function f(x)=−4x2−3x+2 at the point where x=−1. Give…

A: we have to find tangent line to f(x) at x=-1given

Q: 13 Find the secord derivative cy") y= x°+3x - when

A: see below the answer submit the q12 with what to do with the question

Q: Prove, by Showing all steps i that the 1. derivative of arcos x is 1-メ

A: Derivative of arccosx is -1/√(1-x2)

Q: Q2 find the derivative of the following: 1) y = 2stn (5x) 2) y = Inxn cosh 5x ,3) xsin14y = y tan-4x

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost other parts as…

Q: Find the equation of the tangent line to the curve f(x) = x³ln (x + 1) at the point (0, 0).

A: The given curve is: f(x)=x3 ln(x+1)

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

A: Question is solved.

Q: Find the equation of the tangent line to f(x)=-2sin(x) at x=0

A: We have to find the equation of tangent line

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.