Find the equation of the line tangent to the graph of f(x) = – = -3 cos (x) at x = 3 m(x – xo). You should leave your answer in terms of exact values, not Give your answer in point-slope form y – yo = decimal approximations.

Q: 4. Find the equation of the tangent line to the graph of f(x)= 2x² – In Vx at x = 1.

A:

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: Find the derivative of the function. 1 In(1 + 49x 14 y = x arctan 7x dy

A: Given y = xtan-1(7x) -114ln(1+49x2)dydx = d xtan-1(7x) -114ln(1+49x2)dxdydx =…

Q: Find the equation of the line tangent to the graph of f(x) = -3 cos (x) at x 2

A:

Q: 10. Find the 87th derivative of y = cos(2x) at IT

A:

Q: Find an equation of the tangent line to the graph of the function at the given point

A: To find the slope we find y' at x=0, y=0

Q: Find an equation of the tangent line to the curve at the given point. y = ln(x2 − 6x + 1),    (6,…

A: Equation of the line to the curve at the given point is shown below.

Q: #17 Find the equation of the tangent lines LiĦ to y=fCX)= r at x=0 and x=-1 7-3X 2

A:

Q: 9) Find the equation of the tangent line to the function f(x)=-3x² - 2x at the point where x=1. Give…

A:

Q: 5. y= 2arctan(vx)

A: We need to evaluate the derivative of the following function y = 2arctanx

Q: 4. Find the slope of the tangent to y = sin² (2x) at x = 12

A:

Q: Use the chain rule to find the derivative of the function z = x2y3 − x along the curve given by x =…

A:

Q: Find the equations of the tangent lines to the graph of y = ln  x  at x = 1 and x = -1.

A: To find equation of tangent lines at x=1 and x=-1f(x)=lnx

Q: Find an equation of the line tangent to the curve y = (sin x)/1 + cos x at the point ( π/2 , 1)

A:

Q: Find the equation of the tangent line to f (x) = ex at x = 2. Give answer in exact form. x²-1

A: Given : fx=exx2-1

Q: Can you help me step by step?

A: Differentiate with respect to x,

Q: Find an equation of the tangent line to the graph of the function                    y = sinh(1 −…

A: Given curve:

Q: Find the equation of the line tangent to the graph of y = 3x cos x at the point (π, −3π).

A: Given Data: Equation: y=3xcosx Point: (x1, y1)=(π, −3π) The derivative of the given equation of…

Q: Find by implicit differentiation for x2+y2=25 at point P(0,5).

A:

Q: Find an equation of the tangent line to the graph of the function                    y = (cosh x −…

A: We first find the derivative at (0,1) to find the slope

Q: 3. Find the derivative y'(x) implicitly. cos²x + cos²y = = cos (2x +2y)

A:

Q: 2. Find the equation of the tangent line for the function 2 f(x) = x2 + - 3 at a = -2

A:

Q: y = e* (In x)² %3D

A: Here we want to find the first derivative of the given function. For finding the derivative we use…

Q: Find the slope of the line tangent to the curve at the given point. y = 3 cos x; x = 3 3/2 2

A: 1) Find the first derivative of f(x) 2) Plug x value of the indicated point into f'(x) to find the…

Q: Find an equation of the line tangent to the curve y = sin x atx = 0.

A: Solution -  Given equation -  y=sinx At x=0,  y=sin(0)=0 We have - x0, y0 = 0, 0   Equation for the…

Q: Find the equation of tangent line for the curve f(x)=e³x at coordinate (0,1).

A: Given: fx=e3x

Q: Find an equation of the tangent line to the graph of the function at the given point. y = sinh(25 –…

A:

Q: Find the equation of the tangent line to the curve y = 2 + 3 cos x if the tangent line is parallel…

A: We have to find the tangent line to the curve .

Q: b) Find derivative of the following: 1. y= 5x° + 2x -x + x* -9x+12 y=1-cos 20+3sine iI. ii. s= xln…

A: The detailed solution is as follows below:

Q: 1- Solve the second derivative forf(x, y,z) = e sinay3) əx2

A:

Q: Find the equation of the tangent line to the curve tan(x – 1+ 2y) = e + 3x – 4 at the - point (1,0).

A:

Q: What is the equation of the line tangent to the curve e + cos(x) =1 at the point.0 A y=x+ B y=0 y=x-

A:

Q: 6. Find an equation of the tangent line to y = f(x) : = tan¬(2x) at x = 7

A: Given,

Q: Y= In (In2 (1-x))re?

A:

Q: 9. Find the equation of the curve whose y" e*. = - cos x + 6x + 4 with horizontal tangent at the…

A:

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

A:

Q: 4. Find the equation of the tangent line to the curve f (x) = (x² – 4)(2x + 1) at x : -2.

A:

Q: Find an equation of the tangent line to the curve at the given point. y = sin(21n x), (1,0)

A:

Q: Find the equation of the tangent line at the given point. 4x = -5xy + 4y at (1,–4) y = arccos(5x) at…

A: See the calculation below

Q: Suppose the line y = 6x - 4 is tangent to the curve y = f(x) when x= 2. If Newton's method is used…

A: According to Newton's method, if the first root is considered to be x1 then the root of the function…

Q: 12) Find the equation of the line tangent to g(x) = (3x + 11)ex-4 at x = 4.

A: ddxuv=vddxu-uddxvv2

Q: I FIND THE SECOND DERIVATIVE(y") OF THE FF IN ITS SIMPLIFIED FORM 2. Y= 2 Arccos (1-)+ v4x – x?

A:

Q: Find the slope of the line tangent to the curve y = cos2 x at the point(−π/3 , 1/4)

A:

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

A: Given, curve and point

Q: Find the equation of the line tangent to f(x) = cos² x – sin²| %3D at x = 6

A:

Q: 10. Solve for the derivative of y IMPLICITLY 22 + vx³ + 2y= y²

A: Topic =Derivative

Q: 2. Find the equation of the tangent line to the graph of 3x cos y = 1 + x² + /2y+ 1 at P(1,0).

A:

Q: Find the equation of the line tangent to the graph ofy = 3 sin x + cos 2x at x = π/2

A:

Q: Find the slope of the tangent to the curve y=(cos 3x)/( 2-ln(2x+1) ) at x=0

A:

Q: Find the slope of the line tangent to the graph of y = sin-1 x at x = 0.

A: y=sin-1(x)

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: