Consider the function f(x, t) = (x – ct)° + (x + ct)° where c is a constant. Calculate and dx2

Q: Use the chain rule to differentiate f(t)=e^(4t sin(2t))

A: Let us take u=4tsin(2t) and f(t)=y, then we have y=e^u

Q: Given f(x, y) (8a®y + 3xyf). Compute: dx?

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Q: If f(x,y) = x3y + exy^2, find the derivatives of df/dx and d2f/dxdy.

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Q: dy for the implicit function x' +xy - y² = -1 dx at the point (1, 2). Find

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Q: √²¹ fő fő¹¹ (x + y + z) dz dy dx 0

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Q: y=--; x = 2, dx Ax = 2 0. y%3D

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Q: Given the equation x +2xy + y° = 8, evaluate dy Assume that the equation implicitly defines y as %D…

A: The objective is to find the derivative.

Q: Find the cifferential dy of the given funddtion. (Use "cx" for dx.) y- dy

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Q: 7y f(x, y) = tan a² f dx² dy? dzðy dydr

A: From the given problem:   fx,y=tan-17yx   (a) As we know: ∂2f∂x2=∂∂x∂f∂x So, ∂f∂x=∂∂…

Q: Given y= f(u) and u= g(x), find dy =f(g(x))g'(x). dx y39u-1, u= x5 dy -ロ dx I3D

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Q: Rewrite dx d?y + 3 +y: Sin t ニ dt? dt? dx -4X +S = Cost dz? dt

A: the approach follow:

Q: Using the substitutions X = u+2, y=w+2; dx = du, dy= dw, the DE with linear coefficients (x + y-…

A: Using the substitutions X=u+2, y=w+2; dx = du, dy=dw, the DE with linear coefficients (x+y-4) dx +…

Q: Let f(x, y)= Jxy +x+xcos y. (a) Find fy - ở² f_ (b) Find дхду

A: f(x,y)=xy+x+x cos y

Q: Find dy For The Follor dx Functions: b) Jxy +1 -y

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Q: Determine fzz, fyy, and fz for f(x,y,z) = x²y³z – y sin(xz) + e».

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: Identify the parts of DE in terms of their; independent variable, order, and the unknown function.…

A: Given that, There are two differential equation, (a). y'''' + xy''' + x2y'' - xy' + siny = 0 (b).…

Q: Evaluate . y? cos(x) dx + 2ysin(x)dy where C is the straight line between (0,0) and

A: The equations of the straight line joining (0,0)to π2,1 are x-0π/2-0=y-01-0=t(say) i.e. xπ/2=y1=t…

Q: find the values of the derivatives

A: Given: w=z+z first we differentiate given expression with respect to z then substitute z=4

Q: d y is a differentiable function of x . Write dx dy in terms of x , Y , and dx

A: Dear students as per our rule, in one session we can only solve one question. Please post the other…

Q: |e*y dx+e* dy; C: r(t) = (t+ 1, ),-1si<3 Exercise 97.

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Q: dy Find given that dt dx x² + y? = 2x + 4y, x= 3 y = 1, and 7 dt dy i dt II

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Q: Find the differential of the function. y = V6 - t8 dy %3D

A: Solution: The objective is to find the derivative of the given function

Q: dy Assuming - 3x° + 6y + 3xy =0 defines y as a differentiable function of x, use the theorem dx Fx…

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Q: Find for F(X,)= Sin xy+ T Y²-x = 0

A: Given query is to find the derivative of the expression.

Q: The integrating factor of + 2xy= 5x² is dx dy а. b. x? e C. 1 - d. et

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Q: Given the function: f(x,y) = x cos (xy) – x²e*Y - Find fa(x, y) а. b. fy(x, y) a fzy(T, y) C.

A: As per our guideline we are supposed to answer 3 sub parts of a question please repost the other…

Q: dy where C is defined by dx + x2 + y? Evaluate x2 + y? C T(t) =,0 <t< 2n

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Q: FIND dy AND d?y OF x= VI-t AMD y= t° -at dx

A: Given x=1-t , y=t3-3t

Q: dy If x = t – sin t and y =1- cost, then find at t = %3D dx a. -2 b. 0 С. 1 d. 2

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Q: Hw z] Find Sxsin(x)dx using this rule.

A: Given that, Using the chain rule, The integral becomes,

Q: 1. a- Find a result by using variable separation for dy dx b- y³y+x³=0

A: Note:- These are multiple questions and acording to our company guideline we can do maximum 1…

Q: Let X have the pdf 1 p(x) = T(1+ a2)' x E R. %3D Find the pdf of Y = X?.

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Q: F(x, y) = (e5x sin(y))i + (ex cos(y))j

A: The given vector field is not conservative

Q: f(x, y) = 2x- xy + y, find (a.)and (b.) at (Xo, yo) didirectly from the definition. dx dy

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Q: Given the function(x) = x3+ 1, find the ∆y, dy, ∆y-dy

A: f(x)=x3+1

Q: E- Use the chain rule to express dy / dx in terms of x and y: a) y=7+1 and t=2x+1 1 b) y=7+1 and x=…

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Q: of and dy For the function f(x.y) = sin (2x - 5y), find dx of of

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Q: J(y) = (y/(x) + y(x))² dx, for all y E V.

A: In this question, the extremal is given as J(y)=∫01(y'+y)2dx the class  A={y∈V|y(0)=0,y(1)=1}

Q: d y Using parametric differentiation, find dx2 if x = t + 3 & y = t + J5

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Q: dz dz For the function z= f(x.y)= - 2x + 5y? + xy, find f, (5,5), and f, (5,5). dx' dy

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Q: Let f (x, y) = csc(x + y³) ey , find дудх

A: The given function is  f(x,y)=csc(x+y3)exy. The main objective is to evaluate ∂2f∂y∂x.

Q: Use the chain rule to find dz/t. z = x² + y² + xy, x = sint, y = et

A: Here we will find dz/dt,

Q: dy Find - given that dt dx x2 + y? = 2x + 4y, x = 3 y = 1, and 7 dt dy i dt

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Q: ,use the linearity of L   determine L[f]. Q. f(t)=sinh bt, where b is constant.

A: Given, f(t)=sinh(bt), where b is constant To determine L[f].

Q: f(x, y) = sin(z³ – 7y) %3D

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Q: J cos Vx dx X,

A: =?

Q: dy Assuming - 9x³ - 2y - 7xy = 0 defines y as a differentiable function of x, use the theorem Fx to…

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Q: y sin (r²) dt

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Q: dy + y dx dy – 3xy = 5y sin x xy dx2

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Q: f (u) and u = g(x), find dy/dx: a) y = cosu, u = -x/3 |

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…