Q4. If y= f (t) and x=f (t) d²y dx2 dy 3 and %D 4t dx2 dy By using chain rule, find dt

Q: Suppose y = v2x + 1, where x and y are functions of t. dx = 9, find dt dy (а) If when x = 4. dt dy…

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Q: Suppose y = V 2x + 1, where x and y are functions of t. (a) If dx/dt = 9, find dy/dt when x = 4. dt…

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Q: x= t^3 -3t^2 what is dt/dx

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Q: a. By differentiating x2 - y2 = 1 implicitly, show that dy/dx = x/y. b. Then show that d2y/dx2 =…

A: The given equation is

Q: Use Version 1 of the Chain Rule to Calculate dy/dx

A: Given: y=7x-1 We know that ddxxn=nxn-1                                                       ..1

Q: Suppose y = V2x + 1, where x and y are functions of t. (a) If dx/dt = 3, find dy/dt when x = 4. dy…

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Q: Suppose y = V 2x + 1, where x and y are functions of t. (a) If dx/dt = 15, find dy/dt when x = 4. dy…

A: Consider  y=2x+1 where x and y are function of t.

Q: y = 2 (x² – 3x) (a) Find dy/dt when x = 2, given that dx/dt dy/dt = (b) Find dx/dt when x = 7, given…

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Q: Q2) Use the chain rule to express dy /dx in terms of x and y y = sint and t = cos x where t= 0

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Q: d & fle²- · *[e' – In(2t+1)]dt, find g''(x) . dx -2 If g(x) = - A B c) e*- D 4 et + (2x + 1)² e* -…

A: The Leibnitz rule for differentiation under integral sign is,…

Q: If y = x3 – 2x2 + 3 and x = t² + 2 find dy at t=2. dt %3D

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Q: f(x, y) = log, (3x) fe dy In(3x)/(yln(y)2)^2 ||

A: Topic- partial differential

Q: The integrating factor of dx dy 2 y= 3x² is а. b. 1 x С. d. 1

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Q: Q9/ use the chain rule to express dy/dx in terms of x and y and choose correct answer. 1 x = t2 at t…

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Q: 3. fy dy + 10g = e + dt +7 -2t

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Q: what is the dependent variable and linearity of the DE: d(xy)/dx + xy=0?

A: We will find out the required values.

Q: C/ Answer two only: dy dy 1- y= eV1+5x? the dx 3- y= 2r° +3 , x =, he .(using chain rule). dx dy 2-…

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Q: dy dæ 2 and dt at x = 3 if y = 3x? 4. Find dt

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Q: Suppose y = v2x + 1, where x and y are functions of t. dx = 6, find dt dy when x = 4. dt (a) If dy…

A: Given y=2x+1 dydx=dydtdxdt

Q: d²y 2) Obtain a particular solution for d*y dx+ + + y = x³ + 2x +1 dx2

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Q: Q4 Find dy for all of : dx 3 x(x-2) 1- y = xvInx 2- у 3D x2+1

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Q: Find  dy/dt  using the given values. y = x3 − 9X for x = 3,   dx/dt = 2. dy dt =

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Q: If g (x): A d dx [e' — In(2t+1)]dt, find g''(x) - -2 4 (2x + 1)² 4 B (2x+1)² Ⓒe*-In(2x+1) 2 D (2x +…

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Q: 1² + 3x + 4 If t = (r² – 1) what is dt/dx?

A: We have to find derivative

Q: Find dy/dx if y = x^3/2 by using the Chain Rule with y as a composition ofa. y = u3 and u =…

A: a) y=u3 and u=x     dydu=3u2anddudx=ddxx       =12x-12 So, dydx=dydu×dudx      =3u2×12x…

Q: Suppose 4x + 9y² = 36, where x and y are functions of t. (a) If dy/dt =, find dx/dt when x = 2 and y…

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Q: dw if: dt Q1) Using the chain Rule to find w = xy + 3z, x = sint, y 2 cost, z=t (x2 +)

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Q: a) Find if y = (1+2/x)°.x²® using chain rule. dx dy 1-x b) Find if y = using chain rule. dx 1+x

A: (a) To find: dydx if y=1+2x3·x23 using chain rule: Formula used: Chain rule of derivative:…

Q: d²y d²x 9. х y = C1• %D dt2 dt? di 10. L-+ Ri = E. dt 11. (x + y)dx + (3x² – 1)dy = 0.

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Q: If y = (t² + 2t + 6) (3t² + 5), dy find dt dy dt ||

A: Given function: y=t2+2t+63t2+5 We have to find dydt

Q: d If g(x) = - S* [e'− ln(2t+1)]dt, find g''(x) dx -2 2 A ex. (2x + 1)² 4 (В B et + (2x + 1)² Ⓒe*…

A: Given that gx=ddx∫-2xet-ln2t+1dt

Q: Q4) Use the chain rule to express dy /dx in terms of x and y y = sin t and t = cos x where t = 0

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Q: Find d^2y/dx^2 for; x-t^2 y=Dt^5-2t^3+1 *

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Q: Suppose y = V 2x + 1, where x and y are functions of t. %3D (a) If dx/dt = 9, find dy/dt when x = 4.…

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Q: dy = 3 , find dt dx when x = 1 dt x and y are functions of a third variable t. If Væ + Vỹ = 4 and

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Q: f x = 3/t and y = (2t + 1)/4, find (dy)/(dx)

A: Concept - derivative of x and y with respect to  and then divided.

Q: IF V = xsin(y) + ye where x = s + 2t and Y = st Use the chain rule to find dv and- ds dt when s=0…

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Q: dy If y = (t + 6t + 5) (6t² + 6), find dt dy dt ||

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Q: 4. ydx + x(Inx - Iny - 1) dy = 0, when x = 1, y = e

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Q: dy dv 2 Find for y = = [ √3 +4 dt. 0

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Q: dw Q11- express by using the chain rule: dt w = ln(x² + y² + z²) x = cost, y = sint, z = 4√t

A: We have to express dwdtby using the chain rule:

Q: find d^2y/dx^2 implicitly in terms of y and x  2y^3=3x^4

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Q: Find dy/dx and d 2y/dx2 if x = 1 + t 2 and y = tln t.

A: Given: x=1+t2y=t ln t   Chain rule for derivative: ddxf(g(x)=f'(g(x)).g'(x) Product rule for…

Q: Suppose y = /2x + 1 , where x and y are functions of t. (a) If dx/dt = 3, find dy/dt when x = 4. (b)…

A: Differentiating with respect to t, we get

Q: Suppose y = V2x + 1, where x and y are functions of t. (a) If dx/dt = 9, find dy/dt when x = 4. dy…

A: we will diferenciate the equation of y with respect to t, and solve this.

Q: d If g(x) == _S^*[e' − In(2t+1)]dt, find g ''(x) . - dx -2 2 A (2x + 1)² 4 B (2x + 1)² 4 (2x+1)2…

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