12. Let f(x, y) = tan(ry). Find f, and fy for this function.

Q: 3. For the function f(r) = cos(x) find V}(0,27).

A:

Q: 1. If f(x) cos(t) dt, then f'(x) =

A:

Q: 3. Find , 9 for the functions: ax' ây sin(x³ + y* ) x* +y , (x,y) = (0,0) f (x.y) = .(x.y) = (0,0)

A: f(x,y)=sinx3+y3x2+y2, x,y≠(0,0)0, (x,y)=(0,0)

Q: Is there a function f(x, y) such that fx : one. If not, explain the reason = e* cos y and fy : = e*…

A:

Q: If zis implicitly defined as a function of x and y by xy-yz+xz=0, find dz/dx. (y+z)/(y-x)…

A:

Q: ation: tanh’(x² + 3y 3

A: We have to find dydx of following equation. tanh3(x2+3y3)+ex2y4=3        ........(1)

Q: 9. Let f(x, y, z) = xyz=1 and r(t) = (e', t, t²). Find f(r(t)) at t = 1.

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Q: Find the length of the curve y = In sin x from t = -2 to t = 0.

A:

Q: 2²y. 3. Consider the function f(, y) =

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Q: Q2: Find dyidx for the following function:- (1) y = In(x + 4)-xtan (4) y =x*+1) (2) xy + x*y = x +…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 1. Evaluate f[x(1-x*y² +xy )dydx. 01

A: To find the double integration

Q: 1) Find dy/dr by implicit differentiation. tan n'(xy"+y)= x

A:

Q: 2. Let f(x, y) = In(x² + y²). Show that fre + fyy = 0. %3D

A:

Q: If; of t = x then at t=1 is (Note that these functions in N) dx

A:

Q: 4. If f is a differentiable function of x and y with w = f(x, y), x = r cos 0 and y = r sin 0, show…

A: Given: w=fx,y, x=rcosθ, y=rsinθ If w is a multi variable function w(x,y,a,........z) thus the…

Q: 8. Let y -e=y-x²y. Find dy dxlx=1 be a function of x such that e*-y

A:

Q: B) Find- for following functions: дz მა 1) z = exy tan y, x = s + 2t, y = s/t. 2) z = x² + xy + y²,…

A: The objective of the question is evaluate the partial derivative of the given functions.

Q: find ∇f at the given point. ƒ(x, y, z) = 2z3 - 3(x2 + y2)z + tan-1 xz, (1, 1, 1)

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Q: Find the most general antiderivative of the function. f(x) = + 3 cos x

A:

Q: 2. For what value of k will x – iky F(x, y) = (x+ y)² + be analytic?

A: Given function is fx,y=x+y2+x-ikyx+iy If it is analytic then it satisfy C-R equation ux=vyuy=-vx

Q: 2. Show that the function u p(xy) + Vry (y/x) provides the equation = 0.

A:

Q: O Find all second order derivati ves for f(x,y) = Cos(2x) - x²e5Y + + 3y2

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Q: 4. Suppose that F(t) is a differentiable function of one variable. Define the function z(x, y) = e'F…

A: z(x,y) ey F (exy )diff wrt xdzdx = ey F' ex/ye.1/yzx = ey.ex/yyF' (ex/y)and diff wrt ydzdy= ey…

Q: 2 3 tegral of the function xy d by x = 0, y = 0, z = C %3D %3D (2(5)

A:

Q: 4. Find the analytic function whose real part is u(x, y) = e* cos y.

A:

Q: Let = (x – 3)(x – 1)2 for a differentiable function f which is defined on the interval [0,4]. %3D dx

A: TO FIND THE CRITICAL POINTS, INTERVALS OF INCREASE AND DECREASE VALUE OF 'X' AT WHICH LOCAL EXTREMA…

Q: If we use trapezoidal rule for a function f(x) = x +2 1 - , then the approximate of J f(x)dx is…

A:

Q: compute dy/dx for the following function:  y= tan(x2y)= xy3

A: We have to find dy/dx of a curve implicitly.Curve equation is given below:

Q: Let  y = f(x) = x ⋅ cos(πx) Find the equation of the line tangent to the graph of  y = f (x) when…

A: Given Let  y = f(x) = x ⋅ cos(πx) equation of the line tangent to the graph of  y = f (x) when x =…

Q: Q10. Expand f (x, y) = e" cosx about up to third degree terms by using Taylor's theorem for a…

A: The given problem is to find the third degree taylor polynomial of given function f(x,y) about point…

Q: Find domain of following functions In(e*+e) arctan(x+y) x² – y? а. f(x, у) — b. f(x, y) = - Vx - y…

A: Domain of a function is the set where the function is well defined. Thus, we check the points where…

Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = 4

A:

Q: Q2- If Z = f(x, y) = sin(x³y5) Find fyy and fyx

A:

Q: Suppose that f(x, y) = sin(4x + 6y) is a function of two variables. %3D

A:

Q: c) Let f(x, y,z) = cos (xyz)sin(x²y=

A: The given function is f(x,y,z)=cos2(xyz)sin(x2y2z2) ..............(1) we have to find;  fx=∂f∂x=?and…

Q: Use FunCtion 9(x) = - f (X)tZ gra ph Of Y = fLX) to g raph Y=F(x) 2十 -4

A:

Q: Suppose f( – 1) = 2 , f'( – 1) = 3 , and g(x) = r'f(x). The tangent line to g(x) at z 1 is given by…

A: As we know that; The slope of the tangent line to the given curve is equal to the derivative of the…

Q: 1. Find for differentiate each of the following functions. dy хр a) (In(coshx) sinh x) g) y = - b) y…

A: Given: a)lncoshx3c)y+4coshx2=exsin-1(2x)g)y=sinhxex

Q: 2. Let f(x,y)= xe" and find a) fu. fy» fy

A: Please refer the attached image for complete solution.

Q: 1. Consider the following function: y = f(x) = ln (2x² + 6x + 5) , for x >0 %3D (a) Calculate f'(0),…

A: GIVEN: y = f(x) = ln (2x2 + 6x + 5), for x≥0

Q: If z=f(x,y), x= r cos θ and y= sin θ, where f is a differentiable function expressing az/ax and…

A:

Q: 3. Suppose that z = f(x, y) is a differentiable function with respect to variables !! x and y and is…

A:

Q: 2. Show that fxy and fyx are equal for the function f(x, y) = x²y sin(x + y). %3D xy. cos(xry) + 2xy…

A:

Q: Differentiate the following implicit function with respect to x: b. y=-In (Ryx²) + sin(y)e³*xy +e

A: Given

Q: b) Find of the functions: dx 1: f(x)= tan (2x)Vī – 3x² %3D 10 2: x tan y + y" sec x 2x 3: y= csch'…

A:

Q: xyz f(x.y.z) = et ot function is given P(2,,4) in point fux + fyy + fzz colculate.

A:

Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…

A: Consider the curve F(x, y)=0. The objective is to show that if F has continuous second derivatives,…

Q: 2. If f(x, y) is a function of y only, then S" S fdxdy Si fdy. %3D

A: Given query is to find statement is true or false.

Q: Consider function f(x, y) = x cos(TxYy) + x³y. .3,

A:

Q: 9. If f(x,y) = -cos x+e*y, find Vf(x, y).

A: For the solution follow the next step.

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.