Find the derivative of the following functions using implicit differentiation. 1. x^3+y^3-6xy=0 2. y=4(x^2+y^2) 3. y^2-3x+2y=0 Find the slope of the tangent to the curve at the given point. 4. x^2+4xy+y^2=25 at (4,1) 5. x^3+x^2y+y^3=0 at (-1,2)

Q: find the derivative of y with respect to the appropriate variable. 1. y = cos-1 (x2)   2. y =…

A: Part 1. Given,

Q: 1. Find dy/dx if cos 4y+ysin x =3 2. Use implicit differentiation to find the slope of the tangent…

A:

Q: Find the derivative of the function. 1 + x 1 - x y = arctan y' =

A:

Q: Determine the derivative of the following functions. 1. у 3 (8ӕ — 1) sinh(8a — 1) 2. y = (5)…

A:

Q: Find the derivative of y with respect to the appropriate variable 53. у %3D sec (2s + 1) 55. y =…

A:

Q: 2. Use implicit differentiation to find tangent at the given point: (a) xy + y² = 3-3x² at (-1,1).…

A: use implicit differentiation, I try to provide typed solution, if it is helpful like it.

Q: | If In(x² – 3y) = x – y + 3 and y(-2) = 1, find y (-2) by implicit differentiation. y(-2) = An…

A:

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

A: Consider the following equation:

Q: Determine the derivative of the following functions. 1. y = tanh (8x – 3) 2. y = 2x sinh(6x – 5)

A: Here we will use standard formulas for derivative of inverse hyperbolic functions, product rule of…

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

A:

Q: Find the equation of the tangent line to the curve at the given point using implicit…

A: To determine the equation of tangent line to the given curve at point (1, 0).

Q: Find the slope of the curve y2 + x² = y* – 2x at (-2,1) Find the required derivative by applying the…

A: topic - slope of curve note - As per bartleby guidelines ,we are supposed to answer only first…

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

A:

Q: Use implicit differentiation to find the derivative of: 9. х2 +x Arctany %3D у + 4…

A:

Q: Determine the derivative of y=(x−1)4 without using the power rule.

A:

Q: Find an equation of the tangent to the curve x+ Vy = 3 at point (4, 1). [Hint: Use implicit…

A:

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 y given that y = In (sinh x) %3D

A:

Q: Find the derivative of the function. y = tanh6(9x) %3D y' =

A:

Q: Compute the derivative at the point indicated without using a calculator.             y = tan-1 x ,…

A:

Q: find the derivative of y with respect to the appropriatevariable. y = 6 sinh x/3

A: Given function: y=6sinhx3 Using the common differentiation of hyperbolic function: dsinhaxdx=acoshax

Q: find the derivative of y with respect to the appropriate variable.13. y = 6 sinh x/3 14. y = 1/2…

A:

Q: y = |x + Vx + vx y = 3t + /2 + VT-t %3D

A:

Q: Find the derivative of y with respect to x. 1/9x²-1 + sec -13x, x> y= cot %3D

A:

Q: Find the equation of the tangent line to the curve at the given point using implicit…

A: Given equation of curve is (x2+y2-y)2=x2+y2 Differentiate both sides with respect to x.…

Q: Find an equation of the tangent line to the graph of the equation at the given point. x + x arctan y…

A: We can find the equation of tangent line with all steps as below.

Q: Find the derivative of the function defined by the equation x+y=arctan(xy).

A: To find the derivative of the given function.

Q: х3 + у3 %3D бху — 1, (2, 3)

A:

Q: Find the derivative of Vry = -3+x*y° using implicit differentiation.

A:

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. y = arctan 1 + x 1 - X y' =

A:

Q: Find the derivative of y: 1- y = (cos 0)V2 Cos O 2- y = 7sec ln 7 3- y = 2sin 3t

A:

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 the appropriatevariable. y = sec-1 (2s + 1)

A: The given function is y=sec-12s+1.

Q: Calculate the derivative at the point (0,0) of the function given by the equation x=y−2siny.

A: We differentiate both sides with respect to x

Q: Find the equation of the tangent line to the curve at the given point using implicit…

A:

Q: Find an equation of the tangent line to x2 +xy – y³ = 7 at the point (3,2). (You must use implicit…

A:

Q: find first derivative of following function :y sin(1/y ) = 1_xy

A: Use the chain rule of differentiation and differentiate each terms ony by one.

Q: find the derivative of y with respect to the givenindependent variable. y = 2x

A: y=2x

Q: Y3D7

A: One of the method to solve this Question by using logarithmic differentiation

Q: Use Leibniz’s Rule to find the derivatives of the functions

A: Given: y=∫x22x2lnt dt

Q: Find the derivative of the function y = tanh−1(sin 2x)

A:

Q: se 2. Compute the Derivative of the given function and find the equation the line that is tangent to…

A:

Q: find the derivative of y with respect to the appropriatevariable. y = 1/2 sinh (2x + 1)

A: We have to find derivative of y with respect to the appropriate variable: y=12 sinh 2x+1 We know…

Q: Find the derivative of x + y = 10 using implicit differentiation. %3D

A: We have to find the derivative of x2+y2=10 using implicit differentiation.

Q: Consider a function y = y(x) given implicitly by the equation y+ 3y = x. Using the method of…

A:

Q: Show that x + yx−1 = 1 and y = x − x2 define the same curve [except that (0, 0) is not a solution of…

A:

Q: 2 Use the definition of derivative to find the equation of line tangent to f(x) = 2 through x = 3.

A: