For the function f(x,y) = e9xy, find fx and fy. fx = ? fy = ?

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: For f(x) = e+cos(x), calculate f (0) by using the chain rule!

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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: Find dy/dx, where y is defined as a function of x implicitly by the equation below. y3 +2x2 y 5 =1

A: Product rule of differentiation:If f(x) is a function of u and v where both u and v are variables…

Q: Find the linear approximation of the function f(x) = /1 – x at a = 0 and use it to approximate the…

A: Given,

Q: The antiderivative of the function f(z) = + 10z is

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Q: dy from t dx n for y as a function of x, and find two results are consistent by expressing the (a)…

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Q: Given f(z) = x+ VE Calculate the tangent line at the point (16, 20) y : (2- 16) + 20

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Q: Find all stationary points of the function z = f(x, y) = 3x² – 6xy + 2y³.

A: To find stationary points of the function z=fx,y=3x2-6xy+2y3

Q: For the function f(x,y,z) = In (8x + 7y+ 10z), find fy, fy, and f,. fx fy =D Iz =

A: given,      fx,y,z=log8x+7y+10z

Q: Differentiate the function y = e0.4t. dy dt

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Q: For the function z = = f(x, y) = x² − xy² + y³, find the equations of the tangent lines in both the…

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Q: Given the function: f(x,y, z) = x°y2² + æy° +y°z Find а. fazy: (x, y, z) b. fazyz(1, –1, 1) -

A: Given the function :  f(x,y,z) = x3y5z7 + xy2 + y3z

Q: dz Given the function z = xy + y ln|xy|, find ду

A: In this question we have to find differentiation of the given function with respect to y. Formula…

Q: f(x, y, z) = e2* +e3y + e4=

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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: For the function f(x.y,z) = 1 + xy - 5z*, find fy, fy, and f,. fx -ロ fy = =ロ

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Q: For the linear function y = f(x) = 5x+8:  Find df^−1/dy at y = f(10). (f^−1)'(f(10))=

A: Giveny = f(x) = 5x+8Replace x=f-1(y)Nowf(f-1(y))=5f-1(y)+8y-8=5f-1(y)f-1(y)=y-85

Q: Find the derivative of the function f(x, y) 5x2-3y at (8,4) in the direction of A = 3 i-4j O 412 492…

A: First of all we will find gradient, then we will find the directional derivative

Q: Given the graph of f(t) below, f(t) dt = 0. %3D

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Q: dz dz and of the function xsin(y+ z) – xy + z² = 2y. ду -. Find the əx

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Q: Find frx, fæy and firy for the function f(x, y) = (1+x + g)e*

A: Given: - The function is, f(x,y)=(1+x+y)e-xy To find: - The value of fxx,fxy and fyy for the given…

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: Find the following derivatives. where z= e 9x + 4y x = 3st, and y = 2s + 4t Zs and Zt,

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Q: Find of the function f(x,y) = sin(x²y³). əx3

A: The product rule of differentiation : (PQ)'=PQ'+QP' sinx'=cosxcosx'=-sinxxn'=nxn-1 Use the given…

Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. y3 +2x2 y 5=1

A: Differentiate the given equation with respect to x.

Q: Find R of the function Y = f(x) = vx %3D

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Q: The value of b makes the line y = 2x +b be tangent to the function f (x) = x² is O -1 none О 1 O 2

A: Tangent line related problem......

Q: Find the differential of the function. z = 7t − 7/t2

A: zt=7t-7t2

Q: First write the function y = Vx2 +1 as a composition of y = f(u) and u = g(x), and then dy apply…

A: y=x2+1y=f(u), u=g(x)To find:dydx

Q: Q3: Find fyyx & fxyy for the function: f(x,y) = x sin y+ e³

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

Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. −x 4− 5y4 =11

A: We have to find dy/dx of curve equation (implicitly).Curve equation is given by:

Q: Given f(x, y) = y ln(5x 6y), find f-(x, y) = fy(x, y) =

A: The function is given by fx,y = yln5x-6y To evaluate : The expression of fxx,y and fyx,y.

Q: For the function f(x,y,z) = 1 + xy“ - 2z*, find fy, fy, and f,. fx f2

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

A: f(x)=x3+1

Q: Given f(æ, y) = e"" Y' – z°y", show that fæy = fyæ.

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Q: Use an appropriate form of the chain rule to find the derivative. R= e28-t; s = 80, t /2 %3D dR %3D…

A: Given R=e2s-t2 Where s=8∅,t=∅1/2 we need to calculate the value of drd∅ drd∅=dd∅(e2s-t2)…

Q: Find the directional derivative of the function f(x,y) = 3-6xy+ 10y at the 1 point P (1,5) in the…

A: The given function is fx,y=3x-6xy+10y . Obtain ∇fx,y as follows.…

Q: Let f(x, y) = /T²(1 – y²). Find fr (0, 1).

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Q: If f(x) • g(x) is to be integrated with respect to x, taking dx as the differentiated variable,…

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Q: For the function f(x,y) = Əf dx Əf 11 11 4 Əf af find and 2x + 3y' ax dy

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Q: For the function f(x,y) = x e SX, find f,, fy, f,(2, – 5), and f,( – 1, – 1).

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Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. y3+2x2y5=1

A: The given equation is,

Q: Given the function y = x3 + 7x, find the differential dy.

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Q: If y1=2x+4 and y2 =x^2+C, find the value of C such that y2 is tangent to y1

A: Given: y1=2x+4    and    y2 =x²+C   To find :the value of C such that y2 is tangent to y1

Q: Find the G.S. about xo = 0 for: (x² + 4)y" + xy = x + 2

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Q: Find all values of x and y such that fx = 0 and fy = 0 simultaneously. 13. f(x,y) = e*»+y?

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