Let y be a function of x and suppose *= In(x--y'). What is the correct result for the derivative of y with respect to x? dy 2x A dr 2y – x2+y2 dy 2x %D dr x²– y²+ 2y dy x²– y2 – 2x dr 2y dy 2x – x²+y² %3D dr 2y

Q: Find the derivative of y given that y= x In x to ex A None of the given choices 1-In x-x In x B ex…

A: We can find the answer as below.

Q: az Find if yz – In z = x + y ax

A: To find: The partial derivative ∂z∂x, if yz-ln z=x+y. Calculation: The partial derivative ∂z∂x can…

Q: Find the derivative of the function. 3 In (x +8) 5-5x O A. dy %3D dx (x + 8)(5 – 5x)? О в. dy 15 -…

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

Q: Use the derivative rules to write the first step of differentiation. (arctan(x))6 = 6 (arctan(x))5 ·…

A: We will find the first step of differntiation as following

Q: Find all second order partial derivative with respect to variable x and y. F(x,y)= x cosxy + y sinx…

A: We have to find all second order partial derivative with respect to variable x and y: Given:

Q: Find partial derivatives of  hxx ( x,y) , hxy(x,y), hyy (x,y)  For function  h(x,y)= ln ( x^3 +…

A: Given, h(x,y)=ln(x3+y3)

Q: Find the derivative of the function. y = x 5 Vx3+7 O y'=- 2VX3+7 3x7 5x3 Vx3 +7 3x6 O y'=. 5x4 Vx3…

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Q: Find the derivative of y= (2x³+x+1) 4(x²+3)5 (x4+3) 3 O A dy (4) (2x³+x+1) ³ (5) (x²+3) 4 dx 2(x²+3)…

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Q: Find partial derivatives of x3sin y + cos2x tan5y with respect to x and y

A: We have to find the partial derivatives of  x3siny+cos2xtan5y with respect to x and y.

Q: I need help with this question

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Q: Find the derivative of y = f (g(h(3x))). 1. dy = 3 f'(g(h(3x))) g'(h(3x)) h'(3x) A) dx dy B) = 3…

A: Here the given function is y = f (g (h (3x))) To find the derivative of y, we apply the chain rule…

Q: 2.Evaluate the total derivative of u with respect to x for u = 4x4+3y² + 3z² when y = sinx and z =…

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Q: Find the derivative of the function. y=x5 7 3x7 O y'=- 2x3.7 O Y'33 O Y'=. 2x3.7 O Y'=. 3x7 + 5x4…

A: Given, y=x5x3+7

Q: Use implicit differentiation to find the derivative of: 9. х2 +x Arctany %3D у + 4…

A:

Q: independent

A: We will solve the problem.

Q: Find the derivative of y with respect to x. y = tan 1 (In 4x) 1+ (In 4x)2 xV1+ (In 4x)² x(1 + (In…

A: We will find the derivative of y with respect to x as following.

Q: Suppose x and y are variable (y is a function of x) that satisfy the equation Sin(x+y) =xy, What is…

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Q: Find the derivative of y = 4) G* eln sin-) y = G (In-x) sin + V4 – x2. x sin¬1 In sin + (Tx-1 1 y' =…

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Q: Compute the partial derivative fxxyz for f(x, y, z) = cos(cos(x3 + z2 )) + x2 ln(y2 + z2 ).

A:

Q: If f(x, y) = y cos(x) – a° In(y), find the second partial derivative ду дх .A 3x2 = -2y sin(x) ду дх…

A: Option (a) is correct.

Q: f(x, y)= xe"+x sin(xy)+x*y

A:

Q: 2.Evaluate the total derivative of u with respect to x for u = 6x²+4y² + 4z² when y = cosx and z =…

A: We have to find total derivative of u with respect to 'x'    where     u = 6 x2 + 4 y2 + 4 z2  Given…

Q: Determine the derivative of y with respect to x: In x+ In y = x cos y

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find all first and second partial derivatives of f(x, y) = sin(ry)

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Q: f(x, y) = ex + tan(x + y2).

A:

Q: Find both first partial derivative Z = 15x x/y az az ду

A: As we know that: The the Power law: ddxxn=nxn-1 From the given problem: z=15xy

Q: Confirm that the mixed second-order partial derivatives of f are the same. f (x, y) = 7 ln(x² – y³)…

A: This is the question of partial differentiation.

Q: derivative

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Q: Calculate the partial derivative using implicit differentiation of x° w + w® + wz² + 3yz = 0. ди dz…

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Q: Determine the Derivative of the Function: 1. y = ex - 1/ex + 1 2. y = x22x 3. y = 43x^2 4. f(x)…

A: Find derivatives

Q: Find all second order partial derivative with respect to variable x and y. F(х,у)- х сosxу + y sinx…

A:

Q: Let y be a function of x and suppose y= In(y-x). What is the correct result for the derivative of y…

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Q: e derivative of y with respect to x. y= 2sin^-1(5x^4

A: we have to find the derivative of y with respect to x.y=2sin-1(5x4)

Q: By using caushy Rieman find the derivative of f(z) =Iz| if it exit ® fLz) = 2 +Z1

A: It is given that the function fz=z. The function fz=x2+y2. Note that, If the function is…

Q: Use the rules of differentiation to find the derivative of the function y= 3+6sin: a. y' = 3+6cosx…

A: To find the derivative of the below function. y=3+6sinx

Q: Use Quotient Rule to find the derivative. x² + x - 2 3x +1: dy 2x+1 A. dx 3x + 1 dy B.…

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Q: Find both first partial derivative h(x, y) = e-(xª + y^) hx(x, y) = hy(x, y)

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Q: What is the mixed, second order partial derivative of this function. f(x,y)=sqrt(2x^2+y^2)

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Q: Find partial derivative of: z=f(x,y)= e^x^2+y^2  +   cos(x+y^2

A: For this question of partial derivative we need to find out first derivative with respect to x and y…

Q: Find the derivative of y = Arccot (tan(esecx)) in its simplest form %3D A. y' = e Sec*secxtanx B. y'…

A: This question is related to differentiation, we will solve it using given information.

Q: Give one problem for  partial differentiation of function of U with respect to 3 independent…

A: It is partial derivative problem

Q: Find the derivative. 8) y = (x + 1)2(x2 + 1)-3 dy dx dy = -2(x + 1)(x2 + 1)-4(2x2 + 3x – 1) A) B) Y…

A: We can find the correct answer as below.

Q: Find the derivatives of the f: 1. y: sin (x²+3) 6. y= e tan 3x 7. y: e 2. y= tan (4x*) cot (3x-8) 3.…

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Q: Find the mixed partial derivative at the point (2, 3) for h(x.y) = x sin(y) + y sin(x) + xy

A: The given function is, Differentiate the above expression with respect x partially.

Q: Determine the second derivative of 6 y – xy²= I Ay"= 2y³ ( 6 – 2x y)-2 ( 2 - x y ( 6 – 2x y )-1) ®…

A: Let's find.

Q: Use implicit differentiation to find az/əx and əz/ðy. x2 + 4y2 + 7z2 = 4 dz ax az

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Q: Find the derivative of the function. 11) y = cos x4 A) dy -4 sin x 4 B) dY - sin x4 dx C) dy - -4x4…

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Q: Explain of the method of proving the derivative (dy/dx) of y= U(x)"(») where U(x)and V(x) are…

A: The function is, y=U(x)V(x)

Q: If e*cos(y) = e" sin(x), show that dy - e*cos(y)-eYcos(x) e*sin(y)+eYsin(x) 3. dx (a) Using the…

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Q: Suppose a particular investor derives utility function - U(x, y) - from owning x units of stocks and…

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