Q.No.4 Differentiate the following Y= (x²+3)x' Y= ax²+b/ cx Y= 7x*+2x³-3x+37

Q: 1. Find the orthogonal trajectories of the family of curves x? + y2 = cy.

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Q: Find both first partial derivatives.

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

Q: Differentiate implicitly to find the first partial derivatives of z                              xz2…

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Q: Differentiate ysin(1/y)=1-xy

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Q: Find the value of 0z/0x at the point (1, 1, 1) if the equation xy + z3x - 2yz = 0 defines z as a…

A: Given, the equation is xy + z3x – 2yz = 0 and defines z as a function of the two independent…

Q: Find the value of dz at the point (1)1, If the equation 5xy+ z4x -Qy2 =4 %3| defines z as a function…

A: Given 5xy+z4x-2yz=4to determine dzdx  at  (1, 1, 1)

Q: Find all the second partial derivatives of 3 (x,y) = 4r°y– 7xy?

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Q: An economist wants to quantify the offect of olectricity prices on the real economy. By using…

A: Here, since the electricity price jump 27% above their previous peak value and stay at this new…

Q: 2+ yety y' : 2у - хеху

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Q: Find both first partial derivatives. z = cos(10xy) dz az ду II

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Q: 7. what is the durivative oF q= arc cSc V1-3X %3D 3 Cz -Gx)I- 7 X 3. C2-6x)1-3x (-3x)-3x 3 C1- 3x)-3

A: First make it in simple trigonometric functions then diffrenciate it and just put all the given…

Q: Differentiate implicitly to find the first partial derivatives of z                              x2…

A: Given that function, x2 + y2 + z2 = 1 Differentiate with respect to x on both sides,…

Q: 4. xy²1₁ X=1, x = 4, y = 0; about the x-axis

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Q: 2. Find the four second partial derivatives x² +y2

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Q: Find the value of ∂x/∂z at the point (1, -1, -3) if the equation xz + y ln x - x2 + 4 = 0 defines x…

A: Given equation is xz+ylnx-x2+4=0. Given point is 1,-1,-3. Partial derivative of given equation with…

Q: 3.4 Find the first partial derivatives of f(x, y) = 7x°y* + 9x y° +3. df = 21x y" + 18xy dx of %3D…

A: solution

Q: Differentiate implicitly to find the first partial derivatives of z. 11x2 + 5y2 + 3z² = 100 az əx az…

A: Given,  11x2+5y2+3z2=100

Q: fCx)=(1+x)* at X=0 is LUX)=1+ KX + "७) %3

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Q: Find the first partial derivatives of 3x - y f(x, y) = 3x + Y at the point (x, y) = (4, 4). af (4,…

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Q: Find the first and second order partial derivatives for z x2 sin (3x + 2y).

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Q: Find the requested partial derivative. dz z= (3x +4y) ; (2,5)

A: Option D is the correct option. Use the chain rule to find the partial derivative for z w.r.t x.

Q: 4+2x If g(x.y) = By then the mixed partial derivative at the point (- 2. is:

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Q: Find both first partial derivatives. z = 4y²/x az ax az ду || ||

A: z=4y2x

Q: Find both first partial derivatives. z = 2y2√x

A: fx = differentiate with respect to xfy=differentiate with respect to yddxxn=n xn-1

Q: Find all the second partial derivatives forf (x, y) = x³y5 + 2x*y.

A: All the solutions are given below.

Q: +[2yln [2yin (3 3y²dx 3siny dy = 0 ;when x = 1, y = 0 5x x2+3x x+3,

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Q: u = xz siny + yz cosx + xy tanz

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Q: Find the solution of the differential formula in partial derivatives = x³ sent +1; y(x,t);…

A: Integrate twice with respect to t and then put conditions

Q: The

A: Below is sketch of  the given function.    Rotation about x axis will give a volume in 3D plane.

Q: Find the differential equation of the family of parabolas with vertex ar Focus on the x-axis * O y =…

A: We have to find

Q: Differentiate implicitly to find the first partial derivatives of z. 7x2 + 5y2 + 2z2 = 25 az ax dz

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Q: If the curve y = ax^4 + bx^3 + cx^2 + dx + e pass through the point (-1, 8), be tangent to the line…

A: Definition used -           Equation of a tangent line -                         y-y1=f'(x1)(x-x1)…

Q: 5/(A)Evalute ex² dxdy. (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

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Q: Find the first and second order partial derivatives for z = x² sin (3x + 2y).

A: As we know that; The product rule: f·g'=f'·g+f·g' The chain rule: fgx'=f'gx·g'x And The first order…

Q: Differentiate implicitly to find the first partial derivatives of z. 2x? + 5y2 + 11z² = 81 %3D az ax…

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Q: 6,3 + 4x°y +5. 5. 2 Find the first partial derivatives of f(x, y) = 5x°y° + 4x°y +5. af dx II

A: Given: fx, y=5x6y3+4x5y2+5 To  Find: ∂f∂x=?

Q: If z-f (x y): then its total differential can be expressed as * (),中 (). dyds dy + dz O Option 2 O…

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Q: Find all first partial derivatives. z = ln(x2 + y2 + 1)

A: Given The equation is  z = ln(x2 + y2 + 1) .

Q: Find the value of dx at the point (1,1,1) if the equation 6xy + z"x-2yz = 5 defines z as a function…

A: Given: (x,y,z)=(1,1,1) and z=6xy+z4x-2yz-5=0

Q: Use the method of variation of parameters to produce a general solution of the inhomogenous equation…

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Q: (5) Calculate the three first partial derivatives of the following function x²y - 3xz + y2 x - 3yz f…

A: Note: As per our guidelines we are supposed to answer only one question. Kindly repost the other…

Q: 5. Find all the second partial derivatives f(x, y) = 2x + 3y

A: To find all the second partial derivatives of: f(x,y)=y2x+3y For that, find the first partial…

Q: Find the partial derivative of u = x^2 + y^2 + z^2 - 4xyz

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Q: Find * if yz – In z = x +y 3.

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Q: Find the first partial derivatives of 3x – 2y f(x, y) = at the point (x, y) = (1,4). 3x + 2y af…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Make the curve y = ax4 + bx³ + cx² + dx + e pass through the point (1, -8) be tangent to the line y=…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.