Use the Chain Rule for the following questions. Əz 1. Find when z = e' sin(0), r = 4st, and 0 = √√√s² + t² Əs 2. Find du др when u = x + y y + z x = p +6r+ 5t, y = p +6r+ 3t, and z = p +6r - 5t

Q: 2. (8x+²)(8x-6) = 16 then x= 8 A. -8 B. О А ооо B О с co I m 3 с. ; D.3

A: The given expression is 8x+28x-6=16. Find the value of x. As we know exponent multiplies:…

Q: 1.What is the third derivative of y = 2x5 – 2x4 + 5x3 + 6? 2x – 2x + 5x? 40a O A. " = - O B. " 24x +…

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Q: y = x10 + x3. Find y5) (1)

A: Given,           y=x10+x-5

Q: d²y Show that y = sin(2t) satisfies . + 4y = 0 dx²

A: 1) To prove the given equation 2) To find the value of w

Q: 1. Find the derivative of the following 9x²-4x+9 a)y = 2(x²-3)²√√3x-1

A: We know that the derivative of a function fx is the rate of change of that function with respect to…

Q: 7. Find d²y dx² from y = √√x- =√x-²/2

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Q: 6. Find h' (÷) , h" (), and h" (G), given h(r) = sin r cos 3r.

A: since you have asked multiple questions in a single request so we will be answering only first…

Q: Please solve

A: Consider the function

Q: A particle is moving along graph paper in a magnetic field. The intensity of the field at the point…

A: The intensity of field will show steepest descent in the direction opposite to the gradient…

Q: The temperature in an auditorium is given by T = x² + y² z. A mosquito located at (1,1,2) in the…

A: We have to use directional derivative  and direction of maximum change .  direction of maximum…

Q: dx 3.The f to be solvable must be converted to, х2-5х-6 1 а. dx 1 dx - х-6 x+1 1 b. dx 1 dx - - x+1…

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Q: Q53- X--) (xij-Xi - X.j+X)=Zero 13D 「に )に prove that e to

A: We need to prove the given equation.

Q: Use Green's Theorem to evaluate -15/4 O -218/3 O 19/2 [(6y - 9x) dy - (yx - x³) da where C' is shown…

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Q: 1. Find the general real solution for the following di a. r -8r"-9r 18 %3D

A: As you asked solution for part "a" of the question no. 1 , So the solution is given as

Q: (2x + 1)(x – 1) dr 9. 3x + 6 d.x 2.x3 10. | (20 – 1)(x² + 5)dx 17. - (3x – 2)2 - 18. 4x

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Q: 5. Suppose that you were standing at the point (-1,2, 39) on the graph of f(1,y) = r -3ry+4y. If you…

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Q: Differentiate the following:

A: Step 1:Step 2:Step 3:Step 4:

Q: (4x³y*)² (2x?y-)° (6xy ³)³

A: The given expression is 4x3y-222x2y-506xy-33 Use the property amn=amn and a0=1 to get:…

Q: 7. (2x + y + 1) dx + (4x + 2y + 7) dy = 0

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Q: Identify whether or not the following equations are homogenous or non-homogenous /x² – xy tan…

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Q: 4.a) Find d dx y = ln (2²/ n (²x + 5) b) Find dy dx y = 3√√x++2x e³x (5x²)

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Q: Q5. Use the method of undetermined coefficients to solve (a) y" +2y' + y = x²e¬ª. (b) у" — 2у/ + 5у…

A: We are entitled to solve only one question at a time. As the specified one is not mentioned, So we…

Q: Find the equation of the tangent line to (1,2) through the point . x + y + 3xy = 15 that goes Put…

A: Given x3 + y3 + 3xy = 15

Q: 2.2 (x²-y² + sxy + 2) y.dx + ( x + ² + 4xy + 2)x.dy=0

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Q: 3. Consider the function f(t) = 2t? – 3t + 7 on the interval –1 <t <1 with periodicity P = 2 Give a…

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Q: 8. Solve for x. (3r+ 27) (8r-12)

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Q: Q 3. A. Find 1. £(t2 – 4t + 5)u(t – 3) 2. y-y +2y cos 3x - sin 3x 3. E-- s2 s+1

A: