1 For cos2(xy) = , evaluate y' when x = 1.

Q: For which values of x are y = sinh x and y = cosh x increasing anddecreasing?

A: Hence, sinh x is increasing for all x.

Q: Find the particular solution for: y' sin(2y) - cosx = 0, x =when y = 0 %3D 2

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Q: Find dy/dx for y = (cos x) 2 + sin(x 2 )

A: Given that      y = (cos x)2 + sin(x2) We have to find dy/dx .

Q: Find the particular solution for: y' sin(2y) – cosx = 0, x =when y = 0 %3D

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Q: Determine of y = cos(x) – V5a2 In x.

A: I have stated the used formulas in the solution.

Q: Use TWO different methods to find the PS of the IVP: sin x + y cOs x = 0 ( y(7/2) = 2020

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Q: cos² (6y) + sin²(6y) = y + 12.

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Q: 4. Evaluate sin (44°) + COS (290) using differentials. Refer to special triangles.

A: To evaluate  sin440+cos290 using differentials.

Q: 23 Find dy/dx on the graph y3 sec/x2 + y2 = cos2x at point (1, 2).

A: Use product and chain ruleof differentiation at given value

Q: Use Simpson's rule with n = 4 to approximate cos(x) dx 1

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Q: Differentiate y with respect to x where y= cos(-3x2)

A: Differentiate y with respect to x.

Q: 5- = cos nx dx= [cos nx cos nx dx 0.

A: We have to solve given problem:

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

A: The given function is 3y+9x=1

Q: dy 3. Use implicit differentiation to find for x+cos y = xy- 3 dx

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Q: Find integral.

A: We have to find the integral I=∫cos(5x) dx

Q: Find dy/dx if y=(4/cosx)+(1/tanx)

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Q: Calculate for w-z sin(xy+).

A: The given function is w=zsinxy4+9z

Q: A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is…

A: Given a(t)=cos t Integrating with respect to t to get velocity function, vt=∫atdtvt=∫cos t…

Q: Find the family of antiderivatives of f(x) = sin 3x.

A: Given that f(x)=sin3x      ...(1)

Q: 2. Find the derivative (dy/dx) of the following functions: n) y = 1- cos 3x sin 2x + sin 8x tan 4x

A: 2) n) It is required to find the derivative of the function y=1-cos3xsin2x+sin8xtan4x.

Q: Find dy/dx for following functions. 1) y = csc-(e2lnx) + sin-1(2lnv3x)

A: it is given that,  y=csc-1e2lnx2+sin-1(2ln3x) we have to find dydx=?

Q: x/2 | (cos(x) + sin(2x)) dx of

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Q: ayfor gen f(x) = cos (2r + (/2)), a = /4 TT

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Q: for (e3x+y2)5 = sin x cos y, find dy/dx. using implicit differentiation. must show all steps

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

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Q: )if x+tany+ sin-x+ In(yx) +3**1 =4 then find y'

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Q: (b) Show that 2t cos x and sin x = 1 + ? (c) Show that dt dx 1 +

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Q: Let z= sin (y²– 4x). Find the rate of change of z with respect to x at the point (2, 1) with y held…

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Q: 1. Find dy for the following functions : dx Vsin x.cos x 1+2.ln x 3y (ans.: coi x 2 tan x -)) x(1+2…

A: To solve given differentiation easily we take logarithm on both sides and then differentiate it.

Q: Find dy/dx for y=cos^-1(x^1/2)

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Q: find dy / dx for Hhe tellowing in (sec EX) In (cosp?}

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Q: Use the trapezoidal rule withn = 5 to approximate 4 cos(x) -dx

A: To approximate : ∫14cosxxdx using Trapezoidal rule with n=5

Q: 2.Find , if y = sinh x %3D dx' 1+cosh x

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Q: A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is…

A: Given acceleration, a(t)=cost,       t>0 And v(0)=0, x(0)=3

Q: Find the value of parameters € and ¶ that makes f(x)=€x+¶ if x<0 and f(x) =2(¶+€)sin(x) +…

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Q: 1) S ur [sin(In x)+cos(ln x)]² dx

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Q: First and second derrivative of: y=5 /(sin 3x+cos3x)

A: the given function is: y=5sin3x+cos3x we have to find the first and second derivative of the given…

Q: Find dy/dx for 4 cos4 xsiny = 15

A: d(uv)dx=udvdx+dudxv

Q: 4 The range of y =sinx for 7SXS is 2 0syso 4 <ys0 sys1 ys 4 -1sys,

A: We are given a function y(x) = 4/5 sin(x) and we need to find the range of y(x) when π ≤ x ⩽3π2 (…

Q: find dy/dx of y=sin^2 4x+1/2 cos 8x

A: Given,         y=sin24x+12cos8x

Q: Find dy for X=3sec-vE tan (2t) and

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Q: 1) If f(x)= tan(5x), find  f'(5)=??????

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: 2.1 Given that 1 sinh x show that dy cosh a. dx

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Q: Differentiate implicitly to find dy/dx. cos(x) + tan(xy) + 2 = 1

A: Differentiate wrt x

Q: if  x²v+sin(xu)-yv²+u³v=1 x²u-2yv=1 ، cos(xu)+yv=5  ,find dy/dx

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Q: Find at the point (1,0) for cos xy + ye* = 0. dx

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Q: E PARTICULAR SOLUTION OF EVERY EQUATION GIVEN. [tan y – (In x)°]dx = 0 When:x = 1; y = " 4

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Q: Differentiate implicitly for the equation for x^2y+x^3-cos(x)=3y^2

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Q: 3. dy Find if y 2xy - x: dx = cos X using implicit differentiat

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Q: The derivative of : y =0(sin (In (0))) + cos(Im (0)) is:

A: