5. Use the Chain Rule to find dw dt where w = sin 12x cos 4y, x=7, and y =t". :- dw (Type an expression using x and y as the variables.) dx %3D dt (Type an expression using t as the variable.) dw dy (Type an expression using x and y as the variables.) dy %3D dt (Type an expression using t as the variable.) dw dt (Type an expression using t as the variable.)

Q: dw Use an appropriate form of the chain rule to find dt w = 4 cos xy – sin xz; x y = t, z = t8 t'…

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Q: a) L 8(t) cos(48tt) dt b) 8(t – 5) cos(nt) dt c) L[8(t +3) – 28(4t)]dt

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Q: Let w(x, y, 2) = a? + y? + 2? where a = sin( – 9t), y = cos(- 6t), z = e". dw dæ dy dz by first…

A: We have  W= x2+y2+z2  Where , x= sin(-9t) , y= cos(-6t), z= e3t  Find dx/dt, dy/dt, dz/dt and dw/dt

Q: Use the Chain Rule to find dw/dt, where w = sin 8x cos 2y, x = t/2 , and y = t4 dw/dx (Type an…

A: Please see the explanation below

Q: Solve the following problems by applying chain rule. lt dw (a) If w=x - 2y² +z', and x= sint, y=e',…

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Q: dz Use an appropriate form of the chain rule to find dt 1 8 cos x – sin ry; y = 9t t %3D SSEVS Enter…

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 4 cos x – sin xy; y = 7t || Enter the…

A: We have to find

Q: Find d2x/dt? as a function of x if d 6x sin x. dt? ||

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Q: dw Use an appropriate form of the chain rule to find dt 1 w = 4 cos ry – sin cz; x=÷, y = t, z= t8…

A: Given,           w = 4 cos zy - sinxz;            x = 1/t ,      y=t,        z= t⁸

Q: dw Use an appropriate form of the chain rule to find dt w = 4 cos xy – sin xz; 1 x = ; y = t, z = t8…

A: A detailed solution is given below

Q: Find the solution of the following nonlinear ODE through separation of variables given that y(0)=1.…

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Q: dw Use the Chain Rule to find where w = cos 12x sin 4y, x = - dt and y = t". 4 dw

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Q: Consider the following. w = cos(x − y),    x = t2,    y = 21 (a) Find dw/dt by using the…

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Q: Q2) Use the chain rule to express dy /dx in terms of x and y y = sint and t = cos x where t= 0

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Q: (b) Let x1(t) = cos (6tt) and x2(t) = sin(30nt). Determine whether the signal y(t) = x1(t) + x2(t)…

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Q: Solve the following problems by applying chain rule. dw (a) If w=x -2y² +z', and x= sint , y=e', z=…

A: We have to applying chain rule and solve given problem

Q: (a) Evaluate the following derivatives: d ) cos(V5r" - 2)át. s(V5r² – 2)dt . (i) dx J2 d cos V5t – 2…

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Q: tan(): '(), Suppose z = x = u cos(5v) , and y = u sin(5v) . Compute dz/du and az/dv in two different…

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Q: dz 3 Use the Chain Rule to find where z= 2x sin y, x=t°, and y = 3t°. dt '

A: Given,           z=2xsiny , x=t5 and y=3t3.

Q: Find the general solution of du 2u + dt cos t t t

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Q: Find aw/as and ôw/at using the appropriate Chain Rule. Function Values w = sin(2x + 3y) X = s + t, y…

A: we have to find partial derivative by using chain rule

Q: dw where w sin 8x cos 3y, x= dt Use the Chain Rule to find 2 and y = t". dw dt (Type an expression…

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Q: Find dz/dr if z as a two variables function in r and y is defined implicitly by y3 + x22 + r sin r…

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Q: 06: b: dw (1) Find if dt w= w = tanx and x = 4t³ + t.

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Q: Solve the Following Bernoulli Equation dy = y – y² – ya | dt Show ALL Workings

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Q: dw = t³ and y = 7. Find dt Let w = cos(8x - 10y), where x =

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Q: For the functions w = 8x + 3y, x= cos t, and y = sin t, express dw as a function of t, both by using…

A: The given function is w=8x2+3y2, x=cost and y=sint. We have to express dwdt as a function of t.…

Q: 4. g(t) = e³t + cos(6t) – e³ªcos(6t) 5. f(t) = tcosh(3t) 6. h(t) = t²sin(2t)

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Q: as and dw/t using the appropriate Chain Function Values W = sin(4x + 5y) X = s + t, y = s – t %3D TC…

A: Given  w=sin4x+5y   x=s+t       y=s-t

Q: Given that w= x² +y³ +tª, x= siny and y =e'. Which of the following is a correct chain rule for…

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Q: dF find F (x) = J- dx but -x cos(tx) dt t

A: A

Q: 3. Find: d (a) cos(t) dt xp 4

A: The given question is from the topic of Integrals

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 9 cos x – sin xy; x y = 2t t' Enter…

A: This question is based on Derivative.

Q: Let z = x?y + 3xy+ where x = sin 2t and y dz find = cos t. Use the chain rule to when t = 0. dt

A: See solution below. Using definition of chain rule.

Q: dz Use an appropriate form of the chain rule to find dt z = 7 cos x – sin xy; 1 y = 7t Enter the…

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Q: Consider the following. w = cos(x - y), x = t2, y = 1 (a) Find dw/dt by using the appropriate Chain…

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Q: y" + 9y = 5t + 2, y(0) = 2 y'(0) = -1 |

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Q: dw Use an appropriate form of the chain rule to find dt 1 w = 8 cos xy – sin cz; x = y=t, z = t7 t'…

A: Here we have to find dw/dt by chain rule.

Q: (b) Calculate e cos(Tx) dx using integration by parts as many times as necessary.

A: Given: ∫excos(πx) dx The formula for integration by parts is given as…

Q: Given z = sin(1 - 2). x = 2 – ts and y = 2t – s - then calculate when t = -1 and s = -1. dt

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Q: Let T = x²y - xys + 6x, where x = r cos 0 and y = r sin 6. Use the chain rule to find dT/00.

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Q: dw Find using the appropriate Chain Rule for w = cos(4x−4y), where x = tº and y = 3. dt

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Q: Suppose w = 2x2 + 8y², Compute dw/dt in two different ways: x = 7 cos(t) + 5 sin(t) , and y = 7…

A: The chain rule is mentioned below: dwdt=∂w∂x·dxdt+∂w∂y·dydt

Q: T/2 %3D cos (2wt + O, + ©z)dt = 0 -/2

A: The solution are next step is

Q: dw 3) Find ifw = 5 cos(xy) – sin(xy),x = ,y = t,z = t³ - %3D dt

A: Given: w=5cosxy-sinxy, x=1t, y=t, z=t3 For finding dwdt, first we find w in terms of t So, we put…

Q: Find a particular equation for: y(4) + 8y''' + 32y'' + 64y' + 39y = e-2x[(4 - 15x) cos 3x - (4 +…

A: The given equation can be written as, y4+8y3+32y2+64y1+39y=e-2x4-15xcos3x-4+15xsin3x it is also can…

Q: dz Use an appropriate form of the chain rule to find dt z = 3 cos sin ry; y = 7t Enter the answer in…

A: Here, the given functions are: z=3cos x-sin xy; x=1t, y=7t

Q: If z = e* sin y, where x = s?t2 and y = s²t, by using Chain Rule find ôz/ðs and az/dt.

A: Let's find.

Q: Use the Chain Rule to find dw where w = sin 8x cos 2y, x = , and y = t°. dt 2 dw dt (Type an…

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Q: H.W- Compute y( E) with y-J = -8(Sinx+ cosX) 9(T)=0, ý(T) = -8 %3D

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.