If f (x, y) = xe-3y + sin (2x – 5y), then fya=? -3e-3y 10 sin (2x – 5y) -3e -Зу + 10 cos (2a — 5у) — Зе -Зу + 10 sin (2x – 5y) 3e — Зу + 10 sin (2x – 5y)

Q: Evaluate (x²sin y-xcos(y)) dy A x²(1+ sin(1))-xcos (1) + C B x²(1-cos(1))-xsin (1) + C C 2sin…

A:

Q: If y = 12y sin(4z) – 12z sin(4y), then (z, y) = 6y? sin(4z) + 3z cos(4y) + h(x) O (z, y) = 6y²…

A:

Q: Differentiate y = sin(3x + 4y) cos(3x+4y) 1+ 4 cos(3x+4y) з cos(3x+4y) 1+4 cos(3x+4y) cos(3x+4y) a.…

A: y=sin3x+4y

Q: Q#( 1b Compute: [cos (10x)sin²(10x)dx 1 sin°(10x) – A) 30 1 sin°(10x)+C 50 1 cos°(10x)- 1 -cos…

A: We have to solve the given indefinite integral

Q: The f cos 5x cos x dx is 1 {A} = sin 4x - 12 1 1 {B} sin 4x + - 8 12 cos 6x + C cos 6x + C {C} {D}…

A: Given problem:-

Q: Find where z = sin (x²) cos (y) COS © 6.x sin (x²) cos (y²) COS 2.x sin (2²) 2x cos 2.x sin (x²) cos…

A:

Q: tan x dy +y sin x dr = 0, when x = 0, y = | O y (3- cos 21) = 2 O y (cos 2x O y° (2 – cos 2x) = 1…

A:

Q: 1. ƒ(x)=x²- = x² - secx 2. w = ex²-x² + 4x 3. h(z)=In(2z)sin(2z) 3x² 4. y= √x² +1 5. y³ + 2xy = 3

A:

Q: (a) If y = xV², then dy dx (b) If y = (2 + sin 3x)", then d (2 + sin 3x)" = T(2 + sin 3x)=-1(cos 3x)…

A: We have to differentiate the given functions: a If y=x2, then dydx=2x2-1 b If y=2+sin 3xπ,then…

Q: „In sec²(sin2y)dy can be evaluated by writing it as sec2y A sec²(sin2y) - cos2ydy None © In…

A:

Q: 4. y = esec²z (A) sec²rtan resec² z (B)-2 secrtanrx sec²z 5. y= Arccos(x²) 2x (A) √1-2¹ 2x √1-x² (B)…

A:

Q: 1. If f(x, y)=3x' sin y- y² cos x- 2yln x– xh y- 4xy , find- of ôf ô²ƒ ô²ƒ

A: Given: fx,y=3x3siny-y2cosx-2ylnx-xlny-4xy2

Q: Find Domain and Range бяц tue Ⓒsin (x+3) +2y x²+2y 3x + y² 3) 3x + Sin (3x) +2y+Z² Ⓒ x+2y cos2x…

A:

Q: 1. If x - y = 25, then y" = c.) d.) - a.) b.) 2. If y = cos(3x+1), find y a.) 3 sin(3x+1) b.) -3…

A: Authoring guideline: As per the authoring guidelines, we can solve only the first three parts.…

Q: Find y' in y=sin¹ (5x5+2x) + Tan-¹ (x²) 1 1 1+x² -(5x5+2x)² A. y' B. y' C. y' D. y' = = 25x¹+2…

A: Given:y=sin-1(5x5+2x)+tan-1(x2)       y'=dydx=dsin-1(5x5+2x)+tan-1(x2)dx…

Q: Find !V1-cos xdx 2 sin x = 1- COS X V2(-cos x/2)+ c 1/ /2(-cos x/2)+ c В. 2/2(-cos x/2)+ c С.…

A:

Q: Differentiate y=excos(x2): y'= A. excos(x2)-2xsin(x2) B. -2xexsin(x2) C. ex(cos(x2)-2xsin(x2))…

A:

Q: y''-4y'+20y=x^2e^(-2x)sin(4x)-3cos(4x)-xe^(-2x)

A:

Q: дz If x² sin(2y - 5z) = 1 + y cos(6zx) defines z implicitly as a function of x and y, find [Show…

A:

Q: azz = e2x-y + cos(-3x + 2y) + 3x, дхду Given that az where əx 5x2 – sin (3x) when y = 0, and Z =…

A:

Q: Find the iterative scheme for the root of equation sin x-3x +1=0 by Newton-Raphson method. O a. None…

A:

Q: 4. A force of F(x) = x - cos(3x) + 2,x is in meters, acts on an object. Identify the work required…

A:

Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: Differentiate y= cos y2x +1 sin 2x+1 A. V2x+1 sin 2x+1 B. V2x+1 sin 2x+1 C. V2x-1 sin 2x-1 D. V2x+1

A: Please refer the attached image for complete solution. THANK YOU.

Q: The general solution of y"+ 16y=cost is: Select one: a. y = C,cos(4t)+ C,sin(4t) + 1 cost 15 b. y=…

A: Here I am attaching image so that you understand each and every step.

Q: Q2 Q2/If y = (x³ + 5x² + 1)3 + Jsin+/cos³Vtan3x2 find y'

A:

Q: Find dy if y= 5x² sin4x dr O None -20x? cos4x – 10xsin4x 20x² cos4x + 10xsin4x O 10x² cos4x +…

A: We apply u*v rule of derivatives d/dx (u*v) = v*du/dx + u *dv/dx

Q: 4.4 Can you show me all the steps to solve 15?

A:

Q: If  f(x,y,z)=ln(x2y+sin2(x+y))+227x228y2z229,  then    ∂4f ∂x2∂y∂z at (1,1,1)  is equal to

A: See the attachment.

Q: The general solution of y" + 16y3 cost is: Select one: a. y= C, cos(4t) + C2 sin(4t) + 1 -tcost 15 O…

A: Using Solution of Linear Differential Equation

Q: 1. Evaluate f sin*(2x + 3)cos (2x + 3) dx sin(2x + 3) put = t 2. Evaluate f dx Put x2 + 5 = t x2+5…

A: Explanation of the solution is given below.....

Q: Show that y1(t) = cos(3t) and y2(t) = sin(3t) are linearly independent for all t

A:

Q: 2. A. If : = sin(3x+2y) , verify that 2 -3 = -6z ax2 B. If f = x³y3 + 2xcosy + y?lnx then show that…

A: x=sin (3x+2y)

Q: y sin 2x + cos 2y = ax Find y' a – y cos 2x y% = sin 2x – sin 2y а - 2у сos 2x y sin 2x – 2 sin 2y…

A:

Q: If z = 24 - 2x - 6y, x = cos(4t), and y = esint, then dz dt is equal to O-2 sin(4t) - 6esint cost O…

A: Since you have posted multiple problems we will answer first problem for you for remaining problem…

Q: Use Cramer's rule to solve for x' and y' in terms of x and y. x = x' cos 0 – y' sin 0 y = x' sin 0 +…

A: Solution is given as below:

Q: 2. y= 4sin(2x- T) and y= cos(3x-) 2

A: According to question given that y=4sin2x-πy=cos3x-π2

Q: 35. Given that d = 6(sin 2x - cos 3x) and y = 0 dx when x = 0, y = A -3 cos 2x - 2 sin 3x – 3 B 3…

A: We can solve this problem using initial value problem.

Q: B\ Suppose that = 4 cos² t , x = d²y =- V3 sin(2t) and 0 <t <n. Show that sec3 (2t). dy 2 tan(2t)…

A: Dear student, there is a mistake in the question. The second derivative should be…

Q: cos v f(x, у, 2) 3D xz2 af af 2 cos y Cosv siny df = - = - = - dx x2z2' dy dz xz3 XZ af cos v %3D af…

A: Topic:- partial derivatives

Q: y"+4y=sin 2x, where y(0)=3 and y'(0)=¾

A:

Q: 1. dz (1² + 5)² 2. COs z dz 3. sin 3r cos 5z de

A: Given: I1=∫x3x2+52dx, I2=∫excosxdx, I3=∫sin3xcos5xdx

Q: 11 csc²(3x) cot(3x) dx =, (Use Substitution Method) 11 11 +C 6 sin (3z) 6 11 11 +C 6 sin (3z) 6 11…

A:

Q: If it was f(x,y)=y cos(6xy) SO a² f Əy² 2² f Əy² a² f Əy² a² f Əy² = 36 x²y cos(6xy) + 12x sin(6xy)…

A: A detailed solution is given below.

Q: dr 21. (1+x²)/16 – (tan-l r)² dx e2x+2+2 22. 8. dx x2 - 6x + 25 23. 6. 24. dr J (2 - r)V - 4x +3 dr…

A:

Q: Solve the exact DE (2xy³ + cosx tan y +2 sin x)dx + (3x²y² +sin x sec² y-3 csc y cot y)dy = 0 (1)…

A:

Q: If f(2, y) = 3 sin(2x +y) - 4 cos(z- y) then the second derivative f is %3D a. -12 sin (2x +y) +4…

A:

Q: Q# (17' Compute: [tan (10x)sec(10x)dx tan³ 1 tan(10x)+C 10 1 A) tan (10x) – 3 30 1 1 В) sec (10x)--…

A: We use substitution method to solve the Integral.

Q: The general solution of y" + 16y = cost is: Select one: а. v = C,cos(4t) + C,sin(4t) + 1 -cost 15 b.…

A: