Q2: Find dyidx for the following function:- (1) y = In(x + 4)-xtan (4) y =x*+1) (2) xy + x*y = x + 3y (3) Iny = e sinx

Q: Q2/ A/ Show that the functions f(x) = sin-1() and g(x) = 2tan-Vx, have the same derivative. %3D

A: Given : f(x)= sin-1 ( x-1 / x+1 ) g(x) = 2 tan-1 (√x)

Q: (2-4t) sin(팔) V17- cos(27t) 1. Given f(x) = dt, find the equation of the line tangent to the graph…

A:

Q: 7. Differentiate w.r.t x- sin 5x cos 3x 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

A:

Q: 3. Find a result by using exact for a. cos(x + y) dx + (3y2 + 2y + cos(x + y))dy = 0 2)dx

A:

Q: Find y, of (D² + 1)y = sec x = In |cos x| (cos x) - x sin x В y = x sin x + (cos x) In sec x = x sin…

A: Please see the below picture for detailed solution.

Q: 1) Find dy/dr by implicit differentiation. tan n'(xy"+y)= x

A:

Q: dy by implicit differentiation if dx 3 9. = 1. Find - -

A: The given function is 3y+9x=1

Q: what is the derrivative of y^3 + y^2cos(x) = x^3 -3x and what points in the function for dy/dx does…

A:

Q: Find the derivative of cos(0)d0. du Jo cos(0)de = cos (w²) · 2w • d de So" cos(8)d0 = cos(2w) • d S…

A:

Q: 4. Show that 2 s w (b) L(t sinh (wt)) (s² – w²)2 -

A:

Q: Consider the following information fz(x, y) = 2xy - 2r³ and f₁(x, y) = x² + y² – 6. Use the Second…

A:

Q: 1. If y=tanx, prove that y=2(y² +1)(3y² +1).

A:

Q: Find the derivative. (Hint: en a = x) %3D y =S 4 In x et dt O * - 1 4x3

A:

Q: Find the differential d3y of the function y=xsinhx.

A:

Q: 4- Find dy/dx for: d- y = /1+ sin³ (x5) e- y = 2(Va – 1)( f- y = cos³{sin(2x*)} x-2 x²+3x' %3D

A:

Q: 1od of undc cients, obtain the general y" – 2y' – 3y = 2 sinx

A:

Q: (1-1/2 x^2)cos x 3. y = 2cosxsin2x-sinxcos2x 4. y= x^3 - x^2cosx + 2xsinx + 2

A: Differentiation: 1.y=sinx2+cosxdydx=(2+cos x).cosx-sinx(-sinx)(2+cos…

Q: 3. f(x,y) tanx - sec²x - cosy

A:

Q: find dy of X sin 2y =YCO52X

A: Given: x sin 2y=y cos 2x To Find: To find dydx.

Q: 5. Find y', if y = 2cosx sin2x – sinx cos2x day 6. dx if y = 1-cos4x 1+cos4x dx² dy 7. a if y = In…

A: (7) Let y=lnsinh 5θ and x=cosh(4θ)

Q: 2. Evaluate dy and Ay if x = 1 and dx = Ax = 1. 3. Find the equation of the tangent line at x = 1.

A: Your question contain only two which i have solved completely.

Q: If y = sin (4x - 5), then what is y' a. y = 4 cos (4x - 5) b. y 3 сos (4x - 5) C. y' = -cos (4x) d.…

A: In this question  we have to solve the given statements. NOTE: As per our policy we are suppose to…

Q: Q5: Find for the following functions: (4) y = x sinh 2x cosh 2x (3) y = e* sin² x In√x

A: The given functions,3) y=exsin2xlnx4) y=xsinh2x-12cosh2x

Q: S2ta J 2tan x In (cos x) dx=

A:

Q: I Find the second derivative(y") of the following functions and simplify the final results. 1. y =…

A: Given y=lnex+e-x To find y'':

Q: 5. Find the derivatives (a-b) and the limit (c): (2) ± √( 1 cos (1²) dt) (0) ² (154) dt dx 1 r2+x…

A:

Q: The equation of tangent line of the function 36 x3 f(x) e7t dt 36 х at x=1 is Oy- V36 el764 (x-1)…

A:

Q: I Find the second derivative(y") of the following functions and simplify the final results. 1. y =…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Q-1: find the derivative of y with respect to the given indepe 1. y = In(Inx) 2. y = In(In(Inx)) x…

A:

Q: 4. The given equation sinh(xyz) = x+ y + 3z implicitly defines a differen- dz Find ax tiable z as a…

A: Differentiate of sinh(x) =cosh(x)

Q: 12. Find frxyz for f (x, y, z) = sin (3x + yz)

A:

Q: Let e 2* = 2 find dy dx at x = 1

A:

Q: (3) Let 4 = x²y² + x sin y, find 2 dy in terms of x and y; dx (4) Find the equation of the tangent…

A: For the given problem, there are two questions. But according to rules of Bartleby only the first…

Q: dy Find if y = ln x5 + e-cos 2x – In e?. dx dy 5 ,cos?x-sin2 x dy 5 4 sinx cos x = - dx e sin2x-cos2…

A:

Q: (4) 3. Use implicit differentiation to find dy/dx of the following: x2 – 6xy + y3 = 24

A:

Q: Q1) find dy/dx 1) F(x) = sin’2x tan x² x – 3 ) 2) F(x) = sin( x +4

A:

Q: Q1) Use implicit differentiation to find dy/dx if a) (3xy + 6)2 = 7y b) x cos(3x + 2y) = y sin x %3D

A:

Q: 1. If y= tanx, prove that y"=2(y² +1)(3y² +1).

A:

Q: Q2- Find for the following functions :- dx 1- y = (Inx)/tnx 2- y = x cos-1 x - v1-x² +sin-1x

A: We have to find dydx for the following functions... 1. y=lnx1lnx2. y=xcos-1x-1-x2+sin-1x

Q: 1. Find the respect y = 2x5-x² 3x - 20 derivatives with to X using dy using o 12-1

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 1. If f(x, y) = sin(4x-2y)+ln(x²-2y) find fy fyx

A:

Q: y=sin-1x

A:

Q: (a) Find thẻ đéřivătivė. rivative. 1 y = In(x2 – 6) 3 dy dx (b) Find the derivative. 3 = INVX2 – 6…

A:

Q: What is derivative d(y)/d(x) of "xsin(1/y^e)=(1-xy²)^½

A:

Q: Suppose that the tangent line to the graph of y = f(x) at x = 2 is y = 4x – 3 and that the tangent…

A: The given tangent line to the graph of y=fx at x=2 is y=4x-3 and the another given tangent line to…

Q: Find the first derivative 1. y = In v4-x2 %3D 2. In(x2 + y2) + 4arctan = 5 y %3D dy x+4 3. Find , if…

A:

Q: (1) Suppose that y is a function of r satisfying the equation 5x + 10y + 3.ry+ 5y + 6x 0. Use the…

A: