If z = y sin(xy), find at the point (-1,1)

Q: Find dz/ax andðz/@yif I z = x* sin(xy³).

A: If a function f(x, y) is to be partially differentiated with respect to x, then we treat the…

Q: y'sin = y cos a is solvable by?

A: given equation y' sinπx = y cosπx is solvable by separation of variables

Q: x * sin (2y) = y cos (2x) Determine the equation of the tangent at (:).

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Q: Solve the DE: (cos y- cos x)y' +cos y sin 2x=0

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Q: y = sin(x) at |0, 0, with four equally – spaced points

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Q: -을 x e [T, 3 J Sinx =

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Q: x sin wx dx x2 + 6x + 10 Show that (2 sin 3w – 3 cos 3w) w > 0 %3D - 2e2w

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Q: 3) y sin-ly² dy

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Q: Show that both y = sin x and y = cos x satisfy y" = -y.

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Q: If y=(sin3x-cos3x)², find dy dx

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Q: If z = x sin y + y sin x a2z then дхду

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Q: Q1: If Z= x^3+y^4+(x sin y)+ (y cos x), Find Zxx? Zyy? *

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Q: y = x * (sin 1x)² – 2x + 2v1-x² * (sin-1x), Find dy dx

A: Given that equation of y and we find dy/dx. We know that d(sin-1x)/dx = 1/√1-x2. And d(xn)/dx =…

Q: Find the general solution of y′−y=sin x + cos 2x using variety of parameters

A: Given that: y'-y=sinx+cos2x To compare the given differential equation with standard form of…

Q: Find the general solution of y'= sin²xcosy.

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Q: -(sin(xyz)) = O xô zô y

A: Partial differentiation of the function with respect to x means to differentiate the function only…

Q: Determine the General Solution of sin x sin y dx + cos x cos y dy = 0.

A: Given differential equation is sin x sin y dx+cos x cos y dy=0

Q: y = cos(2x), y = sin x, 0<x< 2

A: Solution is given below:

Q: Find d-/dx² at the given point without eliminating the parameter. x=0+ cos0 and y=1+sin0 ; 0 =a/6,

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Q: T c •sinx, S* San* (1 + cosx)dydx 0, 0.

A: Given: The integration ∫0π∫0sinx1+cosxdydx To determine: The value of given integral.

Q: . z=tan 2x dx From their derivatives find

A: Question is solved.

Q: If Z= x³ +y* +(x sin y) + (y cos x), Find (Zxx+ Zyy=?)

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Q: 1 Cos(2x)dx 0. (i) Using composite Trapezoidal rule with n = 2, 4

A: As per the policy of bartleby the provisions is to solve only one question at a time So I am solving…

Q: Find the equation of the line tangent to the cardioid r = 1+ sin(0) at Ô0 =

A: Given that,, Here, differentiate w.r.t. ,we get, We know that, To find: equation of the line…

Q: 9. Find dy for y defined implicitly. by the equation xy-secly)-3x

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Q: 17. Determine the value of fx dy - y dx, where x(t) = (cos 31, sin 3r), 0 ≤ ≤n.

A: The given integral is: ∫X x dy - y dx, where Xt=cos 3t, sin 3t, 0≤t≤π The components of the…

Q: w= Cos (x+y) + Sin (X-4) Show that dy?

A:

Q: Findəz/əx andəz/əy if z = x* sin(xy³).

A: Find ∂z∂x.

Q: Find the linear approximation to h(y)=sin(y+1) at y=0. Use the linear approximation to approximate…

A: Recall that the linear approximation of a function y=f(x) at x=a is given by y=f(a)+f'(a)(x-a) Here…

Q: • If y = cos x2 + x² then y(4) = 8x? sin x² + 0 TO F

A: Topic- Derivative

Q: g(x, y) = 9x sin(x²y) Calcule 9ry

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Q: d'y +2 sin y cos' y = 0. dx 6. If y= tanx, show that

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Q: What is the first step in eliminating the parameter t from the equationsx= 3 1 sin t and y = cos t -…

A: Given equations are x=3+sint,y=cost-2. To eliminate t from given equations, substitute values for t.

Q: tan '(z) Find for y = In( - dy dz You do not have to completely simplify!

A: topic - derivatives

Q: Find if y%3D cos (2x)+ 2еж: dx dy

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Q: dz Find x? sin(2y – 5z) =1+y cos(6zx) -

A: This is partial derivative so differentiate it as normal differentiation of z with respect to y…

Q: Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); i и

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Q: Find the value of zrr at the point (0, 3, 2) where x?y? + z2 – cos(xyz) = 10. -

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Q: What is if z = x'y+ sin(xy²)?

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Q: If y3 + y = 2 cos x, find the value of d2y/dx2 at the point (0, 1).

A: given, y3+y=2cos xwe have to findd2ydx2 at point (0,1)

Q: If y = (sin-' x)², show that (1 – 2*) dy dr? dy 2. dx

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Q: if z=ex( x cos y-y sin y ), show that  ∂2z/∂x2+∂2z/∂y2=0.

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Q: y = cos x, y= sin 2x, x = 0 and x = 2

A: Solution

Q: cos y f(x, у, z) -D xz2 XZ

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Q: Use differentiation rules to find y' = dy/dx.

A: Given,

Q: Find the value of zr» at the point (0, 3, 2) where a²y² + 2² – cos(ryz) = 10.

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Q: Find the differential of the function. y = 6 sin(60) dy

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Q: If Z= x^3+y^4+(x sin y)+ (y cos x), Find Zxx? Zyy?

A: Partial derivative of a function of two or more variables with respect to one variable is the…

Q: Find the length of the curve y = ln (sin x), π/6 ≤ x ≤ π/2

A: Given y = ln (sin x), π6≤x≤π2

Q: Find the derivative of the following functions/parametric equations. 4. e2x cos y + y2 = 1

A:

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.