calculus Find the equation of the tangent line to the graph of f(x) = 4 - x2 at point (1,3).

Q: Finding a Derivative In Exercises 13–32, findthe derivative of the function. y = 5(2 − x3)4

A: We have to find the derivative using the chain rule of differentiation . According to the chain rule…

Q: Using the Product Rule In Exercises 5–10,use the Product Rule to find the derivative of thefunction…

A: According to the product rule of differentiation , The differentiation of the functions of the form…

Q: Find an equation of the tangent line to the curve at the given point. y = 6ex + x,  (0, 6) y =

A:

Q: Use second fundamental theorem of calculus. Find the derivative F'(x) of the function.

A:

Q: Finding a Derivative In Exercises 13–32, findthe derivative of the function.…

A:

Q: derivative of (√2)^csc4x

A:

Q: derivative of the fun x + 2 y = e y' = %3D

A: We are asked to find the derivatives of the function.

Q: Find an equation for the line that is tangent to the curve y = 2x3 - 8x at the point (2,0). (Type an…

A:

Q: Finding a Derivative In Exercises 7–26, usethe rules of differentiation to find the derivative ofthe…

A: y=x7

Q: Derivative of y = (x(1-x^2)^3)/((1+x^2)^1/2)

A:

Q: equation of the curve at every point of which the tangent line has a slope of -e-².

A:

Q: Finding a Derivative In Exercises 7–26, usethe rules of differentiation to find the derivative ofthe…

A: Given: 9. y=x7

Q: Derivatives of Functions Find the derivatives of the functions in Exercises 1-40. 34. y = 4xVx + Vĩ

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: QI. Find the length of the of the curve from x = 0 tox = 3.

A: First differentiate  wrt xand then use formula

Q: Explain your understanding of the connection between the derivative of a constant and the slope of…

A: We need to establish a relationship between the derivative of a constant and the slope of the…

Q: f(x)= (3x²+2x+1)

A: Topic = Derivative

Q: Finding a Derivative In Exercises 13–32, findthe derivative of the function. y=\frac{1}{x-2}

A: The rate of change in the value of the dependent variable with respect to the change in the value of…

Q: Linearization based at a uses a tangent line to a curve at x=a to estimate the y-values of a…

A:

Q: funchoN fo -2x3 + lox218X nd the derivativef"x)=

A: Given f(x) = 2x3 + 6x2 - 18x - 54f'(x) = 6x2 + 12x - 18

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: Direction: Find the equation of the tangent line to the function at x=a. 1. у %3D Зх-1 at x = 9 x+2…

A: We know, the equation of the tangent line to the function f(x) at x=a is given by y-f(a) =…

Q: Use part one of the fundamental theorem of calculus to find the derivative

A:

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

A:

Q: e equation implicitly defines y as a differentiable function of >

A:

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

A: Differentiability and Continuity

Q: Find the point on the curve y=e3x where the tangent line passes through the origin

A: Given: y=e3x. let's that point on curve is a,e3a so, slopem of tangent is given by dydxa,e3a and…

Q: Using derivative Find the slope and the equation of the tangent line to the curve y=x²+1 at x=0.…

A:

Q: Find the equation of the tangent plane to the graph of 5y f(x, y) at the point (4, -7). (Use…

A:

Q: Line IB and line IA are both tangent lines. IB = 2x - 5 and IA = x + 15. Find the value of x. x+15…

A: from a given point length of tangent is equal.so IA=IB.so x+15=2x-5,x=20

Q: Finding a Derivative In Exercises 5–26, finddydx by implicit differentiation. 5. x2 + y2 = 9

A: Implicit differentiation:       Implicit differentiation is the procedure of differentiating an…

Q: Finding a Derivative In Exercises 7–26, usethe rules of differentiation to find the derivative ofthe…

A: Given function: y=x12

Q: Find the equation of the tangent line to the curve y = 2x +x-1 at the point (3, 20). %3D The…

A: The given curve is y=2x2+x-1. Find the equation of the tangent line to the curve y=2x2+x-1 at the…

Q: uation of the tangent line to the curve at the given point. = (1 + 2x)9, (0, 1)

A:

Q: Does the graph of -1, x0 have a vertical tangent line at the origin? Give reasons for your answer.

A: Given function is fx=-1, x<0   0, x=0   1, x>0.

Q: Direction: Find the equation of the tangent line to the function at x=a. 3. y = V5x + 4 at x= 1 4. y…

A:

Q: Point Tangent line Function (1,0) 1. y = x* - 3x? + 2 2. y = x³ - 3x (2, 2, ) 2 (1,2) 3. f(x) = 4. y…

A: A  tangent to a curve is defined as a line that touches the curve at only one point. The slope of…

Q: Find the equation of the tangent line to the curve y = (x- 1)°(x+ 3)² at the point (2,25). The…

A: Firstly ,find the derivativw of y and then put the value of x coordinate of point to find the slope…

Q: Estimate the slope of the tangent line to the curve at the given point (x.y). The slope of the…

A: NOTE: Refresh your page if you can't see any equations. . choose any two points from the tangent…

Q: Direction: Find the equation of the tangent line to the function at x=a. 5. y = 2x³ + 4x²+7x-9 at…

A:

Q: Finding a horizontal tangent line Determine whether the graph ofƒ(x) = xx, for x > 0, has any…

A: Given: y= f(x) = xx , for x>0               Now,                                      lim  x→∞…

Q: differentiation- Can you have an y variable in your answer,

A:

Q: Find the equation of the tangent line to the graph of the function f(x)=(x^2+9)(x-3) at the point…

A: Given : f(x) =(x2+9) (x-3)

Q: Find the equation of the tangent line to the curve y = (x- 3)° (x+ 5)² at the point (4,81). The…

A: Solution:- calculate slope

Q: Evaluating a Derivative In Exercises 65–72, find and evaluate the derivative of the function at the…

A: remember this:…

Q: how do you find the  (a). equation of the scant line through the points wehre x has the given…

A: The given equation is f(x)=x^2+2x.

Q: -9) √(x+2)]2

A: The function given is , fx=x2-9x+22. To find the derivative of the function, Apply the product rule,…

Q: ain the rule of maximum and minimum using Derivatives with an example?

A:

Q: QI:Find an equation for the tangent to the curve at the given point. 2.y = (x – 1)2 + 1 (1,1)

A: This question is about application of derivative to find tangent to given curve

Q: quation of the tangent line to the curve at the given point. y =    2 + x3,    (−1, 1)

A: