6. Let z = 5e** sin y . Compute the differential dz. A) dz = 20et* sin y dx + 20e** cos y dy B) dz = 20e" sin x dx + 20e³" sin x dy C) dz = 20e** sin y dx +5e** sin y dy D) dz = 20e** sin y dx +5e** cos y dy E) dz = 20e** cos y dx+ 5e** sin y dy 4x

Q: dx 1)y /sec(3x) 2) y = Vu + 2u , x= u? - 3u

A: Definition used -            Chain rule of derivative -                             ddx(f(g(x))=…

Q: dy B) Find for all the following dx 1) y = sin-13x 2) y = In(5x) 3) y = Vtanhx

A: Solution: As per our guideline we are supposed to answer only first three question please repost…

Q: * Find dy/dx for the function y=2 sin(3x) cos2x 4 sin (3x) sin (2x) - 3 cos (2x) sin (2x) O 6 cos…

A: We know that derivatives  general power rule is - d(xn)/dx = nxn-1. And d(sinx)/dx = cosx ;…

Q: 11. Integrate the function. y? -dy (49 – y² ) 5 y 7y +C - sin"' y + C V49 – y V49 – y² V49 - y -…

A:

Q: Find dy/dt and d^2y/dt^2 for function aln(y)+b cos^2(ty)=2t^3 where a  and b are certain constants.

A: Derivative two times simultaneously and use the forma for derivative

Q: 3 tanx dx 3/ secx

A: Indefinite integral: An integral which does not have any upper limit or lower limit of integration…

Q: 3 z'= 2(x"+Z) Arrang e in linear form: dy Q) or dx

A:

Q: Find dy/dx by implicit differentiation. 6) x3 + 3x2y + y3 = 8 dy A) dx x2 + 3xy B) dy dx x2 + 3xy x2…

A:

Q: 을(22 + y7) %3D (25) d. da da d 을 (2) + 옮 (v?) 3D0 d dæ da a function of x and using the Chain Rule,…

A:

Q: Let h be a differentiable function of x obtained from the parametric equations a = f(t), y= g(t) .…

A: if x=f(t) and y=g(t) thendydx=dydtdxdt

Q: -x-1 a) y' = +2yi-1 v(0)=1

A:

Q: tan y dy + In (secy) In (6)sec® de

A: Given data:     The given integral is: . The given integral can be written as, Assume Let…

Q: Consider y=(x2+1)2x a) find dy/dx b)Evaluate y'(1)

A:

Q: iv is analytic = -11..

A:

Q: y = cos“ x, Find dy/dx O dy = - sin(x*) O dy = 4 cos3 x sin x dx O dy = - 4 cos x sin x dx O dy = -…

A:

Q: What is the derivative y^2 = 64 with respect to t? O 2x dx/dt + 2y dy/dt = 0 O 2x dx/dt + 2y dy/dt =…

A: Given that,  x2+y2=64

Q: S*(1+v*) -\dv (cot-ly2) 2.

A:

Q: determine the relation x^2 + y^2 = 13. dy/dx in terms of x and y using implicit differentiation.

A:

Q: x2 + 8x +3 10) y=- _ dy A) 3x2 + 8x - 3 dx X Find the derivative. A) 11) s= t3 tan t-√√t ds dt C) dy…

A:

Q: Use logarithmic differentiation to find. ○ A) dy = 3 (²)² 2 dx sinx O B) 4 = ()() 3 (senx)² (cost dy…

A:

Q: 1/2 yee? +4 dy +17y=0 dx2 when Pove then ydy that Sinzx, %3D0 dx

A:

Q: What is the first-order derivative of y = x^y?

A:

Q: 8) a) Find dy/dx if: e3x = x+y b) Differenctiate y = (sin r)"

A: We know that general derivative of d(xn)/dx is nxn-1. And derivative of d(sinx)/dx = cosx  d(lnx)/dx…

Q: 3. f sin³y(2-3cosy)² dy

A:

Q: ul)= F sin (rch Sin ht) sinh(u) ult) dot Sin h1 Sin hCm) Sin h(tal) uGt) It ula) = a ( Sinh!

A: Consider the given information: Let u(x)=Fsin(nπ)x           ..(1)…