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

A:

Q: Please solve

A: Consider the function

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

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

A:

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

A:

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

A: