dy 12. dx Va? – x2, (a is a constant)

Q: f"Ve-1) de (e* a) (e ) da Ante 1) de Bos birak

A: The volume of the solid formed by revolving the region bounded by the curve y=f(x) and the x−axis…

Q: Q22. If y=tan x+ tan dy is: -then dx 2 (d) 1+x (a) 0 (b) 1

A: Given function is                                          y=tan-1x+tan-11x we have to find…

Q: (c) Given tanh (x) + tanh (y) = 1, show that, dy 1- y? dx 1- x2

A:

Q: dy satisfies dx? 2 iven by

A:

Q: dx x2+y?, dt dy 2, find dt dL when x = dt If L = V -5, and 7 and y = 6. dL dt

A:

Q: Show for Re(z) > 1 dx = r(2) ((2). et - 1

A:

Q: dy when t = 7. dx Evaluate y = 2z? – 3z + 5 x = 4t +t t = z? +z+1

A:

Q: dy| 2х — 6 - Find- , where y = dx\x=1 x + 2 Enter the exact answer. dy dx=1

A: Solve

Q: dy is let y = ln(V – 9 + a). -9+x then dx S'

A:

Q: x³ ex? dy y In y 2. dx ||

A: Given:                dydx=x3ex2y ln y Simplify:              y ln y dy=x3ex2 dx Integrate both…

Q: If x = 2t2 +t+1 and y=8t3+3t? + 2 then dy at t = 1 is dx

A:

Q: dy Given that y = 5u+ 4 and x = -u', hence find dx

A:

Q: T rsinx S"Stnx y dy dx 2 dx dy

A:

Q: dy Find the value(s) of dx at y=1 given that x2y+y2 5. ony A only -클 only 3. D 2/3

A:

Q: SOLVE THE FIRST ORDER DE. dy – yln(yecosx)dx = y sinx dx

A: dy-yln(yecosx)dx=ysinxdx

Q: dy Determine given: dx ax*y³ – bxy = 36 where a and b are constants.

A: We can find the dy/dx as below

Q: dy 1. Obtain from the following. dx 3at? y = 1+t3 3at x = (a is constant) 1+t3

A:

Q: - 16y? – 16x – 16y = 0. dy at the point (3, dx ves to calculate

A:

Q: dy In |= 8x+7y; y(0)=0 dx

A:

Q: d'y Find dx? given that 5xy = 25. Oa. O a. dy 2y 2 dx2 Ob. d'y 2y x2 Oc. d'y ,2 dx? O d. dy dx?

A: Topic:- Derivative Correct option = b

Q: (b) Given that y(6x +1) e** = 1+ - In dy Find when x 0 and y=1. dx

A:

Q: If y = In(x² + 5) + sinx function then ay at x = 0 is ? dx 11 10 1 10 O 1 O 5

A: Given, y=lnx2+5+sinx  We have to find  dydx at  x =0

Q: x +1 dy =? find y = In x – 1 dx

A:

Q: QA1 (a) Given that y = (3+4x²)° +10sin(5x) determine dx dy

A: The solution is given below  Please post separately

Q: 3.) y tanʼxdx +ln* ydy = 0 dy_ (y?+4) Inx In (y?+4)Y 5) dx

A: y tan2x  dx + ln4y dy = 0∫-tan2x  dx =∫ ln4yy dy∫(1 - sec2x) dx  = ∫ t4 dt   (where, t = ln y)Hence,…

Q: Prove the general formula

A: Consider the given integral ∫dxx-ax-b First, decompose the partial fraction  1x-ax-b=Ax-a+Bx-b…

Q: dy when t = 7. dx 13. Evaluate y = 2z? – 3z + 5 x = 4t' +t t = z? + z+1

A: Derivative of the function decides whether the function is increasing or decreasing. If the first…

Q: dy Find for dx 4) y= sinxtanx

A:

Q: dy 4 sin 2x, y = 2, when x = 1/2 dx

A:

Q: Evaluate dy/dx when t = 7 such that: y = 2z^2 - 3z + 5 x = 4t^3 + t t = z^2 + z + 1

A: Given                y=2z2-3z+5           (1)    x=4t3+t                   (2)    t=z2+z+1…

Q: Evaluate the integrals

A:

Q: dy if y = vt' -e' and x = dx Determine In(6t)

A: dy/dx = [7/2 t^5/2 - e^t] [ln(6t)]^2/ t^2 [3ln (6t) -1]

Q: dy Q4: If y = tanh e3x find dx

A:

Q: S dy S f(x, y)dx

A:

Q: LL y e* dz dx dy -Inx

A:

Q: dy dx || X x² + 100

A: We have given differential equation  dydx=xx2+100 dy=xx2+100dx Integrating both sides…

Q: y = sinx + x² to dy dx? x² y +2

A: Given, y=sinx +x2 Differentiate two times with respect to x to get required differential equation.

Q: (2)S. dx where c = constant 0 cx let c-x = e-x In c

A: We use the definition of the Gamma Function to solve the given question.

Q: dy Given y= 5e3X + sin x, -is dx

A: differentiate y with respect to x  with the help of differentiation properties we will solve the…

Q: dy 1 dx sec?y

A:

Q: Find the value(s) of dx at y= 1 given that x²y+y² = 5. only В only 2

A:

Q: O O O OO dy Estimate dx of the function y = 3 –x². -1 O a. 6 b. 1 с. 2 O d. 3 e. 0

A: 1.   The given function is y=3-x22.   The given function is s=2t+t2

Q: dy If y=t+t and x= 5t+7 then at x = 17 is: dx

A:

Q: dy 4. = 4 sin 2x ; y = 2, when x = Tt/2 dx

A: Given a differential equation, dydx=4sin2x ; y=2 where x=π2 To find the general solution of the DE.

Q: Q2. Find of y = 4x/x + V at x = 1? dx

A:

Q: 56. Given that x+y - xy and that y dx dy when x 1 show that xy = e*

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: (c) Given tanh (x)+ tanh¯'(y) =1, show that, dy 1- y? dx 1- x2

A: The given function is: tanh-1(x)+tanh-1(y)=1