In Exercises 1-8, use the given substitution and the Chain Rule to find dy/dx. 1. y = sin (3x + 1), u = 3x + 1 2. y = sin (7 – 5x), u = 1- 5x 3. y = cos (V3r), u = V3r 4. y = tan (2x – x), u = 2x – x sin x sin x 5. у 1+ cos x 1+ cos x 2 6. у 5 сot 2 7. y = cos (sin x), u = sin x A 8. y = sec (tan x), u = tạn x can

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A: Given: I=∫cosxe4+sinxdx  ....(1)   We know that; ∫eax+bdx=1aeax+b+C

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Q: 2. Find an interval where f,(x) = sin2 x and f2(x) = cos² x are linearly independent. %3D

A: W(π/4) = -sin(π/2) = -1 W(π/6) = -sin(π/3) = - √3/2 Since, Wronskian is not zero for a single value…

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A: We have to give an example of a value of z such that the equation sinx=z is unsolvable.

Q: The function y = 2x – cos x have two variables (x and y), these variables called

A: Here, the given equation is y=2x-cosx , which is a function of two variables(x and y). The name of…

Q: 2. 2 | sin xcos xdx

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Q: Qlif y= fcus and u=x46x +5 U =X and - 2u -1, Sind dy dx

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Q: Find sun alpha and tan alpha if the terminal side of alpha lies along the line y=-8x in Q2

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Q: evaluate

A: Given integral is evaluated as follows.

Q: 2) Proof that If y = f(x) = = cos x then dx sin x

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Q: [(1+cos 3x) dx 3x)?dx + cos

A: Given: I=∫(1+cos(3x))32dx

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A: u.v rule for differentiation, d(u.v) = u.d(v)+v.d(u)

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Q: w= Cos (x+y) + Sin (X-4) Show that dy?

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Q: Use an appropriate form of the chain rule to find and if z = xe" , x = 2uv , ди y = sin(uv). You…

A: By using the definition of  chain rule for two independent variables we find the value of ∂z∂u, and…

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Q: Using the substitution t tan can be written as of dx sin(x) - 60 cos(x) of dt +30-30 2 de 30²2²…

A: I am attaching image so that you understand each and every step.

Q: ,2 Compute x² cos(x³ + 3) dx

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Q: Compute cos æ dæ. cos x +C 3 cos a sin x +C sin r cos a + cos x +C sin a +C 3 sin r + sin I 3 sin a…

A: Given, ∫cos3x dx We can write it as by using the trigonometric identity as, cos2x=1-sin2x∫cos3x…

Q: 1/w cos Tº If h(w) = 10 -dz then h'(w) = (m),4

A: Given:-h(w)=∫101wcosx9x2dxTo find: h'(w)

Q: satisfied

A: We will solve the problem.