2. If w In(4xy) = 2 - cos(2yz — 3), x = log(t), y = = : 4eª² and z = sin(ț³ – 1). Find dw dit

Q: If z = ln(2x+y), x = u sin v, y = v cos u, find az/av when u = 0, v = 1. A. -2 B. -1 C. 0 D. 1 E. 2

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Q: 8. (t² + 3) cos(5t) dt

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Q: . If y = tan( sin t (. cos t-1 1 dy %3D show that dt 2

A: The given details are as follows. y=tan-1sin tcos t -1 Observe the chain rule of differentiation as…

Q: 2. Which of the following functions is of exponential order? * 4 f(t)= Sin 4t f(t)= 5{VT + A.) O B.)…

A: The function of exponential order is determined as shown below.

Q: d d. dx tan(t)dt

A: Leibnitz Rule of differentiation :     ddx ∫α(x)β(x) f(x,t) dt = ∫α(x)β(x) d(f(x,t))dxdt +dβ(x)dx…

Q: If x = t + 2 sin(at), y = 3t – cos(nt), evaluate at t =;

A: Given that x=t+2sinπt, y=3t-cosπt, we have to find dydx at t=12. Now, dydx=dydtdxdt…

Q: If x=t² - 5t and y=1-61² , then dy at t =1 is dx Oa. 4 O b. -1 - 4 d. 4

A: We need to find parametric differentiation

Q: fip Find or y' of the following functions and make any obvious simplifications: dx a. Y = arctan(e")…

A: Find derivative of the following using the properties of the derivatives

Q: 1. S dr 1+sin a+cos a

A: The solution is given below in the next step:

Q: 9. Find if x (t) = t + sin(t), and y(t) = t - cos(t). doe

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Q: Let a > 1 be a constant and y = (9e- sin z 3) In(x+a). Find y'(0).

A: Product rule of differentiation:…

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

A: As indicated in the question, we will make use of chain rule of differentiation. Recall that the…

Q: S sin(x - 1) cos(x² 2 + 7Jdx

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Q: 1/2 sin 12 y cos' y dy y

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Q: Calculate L{e-# cos(2t – r)}

A: We have to calculate : Le-2tcos(2t-π) First we will calculate , Lcos(2t-π)…

Q: 3. If y = w sin w, then what is dy/dw??

A: y=wsinwTo find d2ydw2

Q: Find , if y= cos"(2x) + 2e*c* dx sec x

A:

Q: \lim_{x\rightarrow 7}\frac{x^2-5x-24}{x^2-4x-32}x→7lim​x2−4x−32x2−5x−24​

A: find out the limits of  a)limx→7 x2-5x-24x2-4x-32 b)limx→7x2-4x-32x2-5x-24

Q: 1. [a4 In xdx

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: o(e) = La t -Va V1 + t²

A:

Q: 3. Calculate L {e=# cos(2t – 7)} COS

A: Given function is as below :

Q: If 2 cos(y2)dx - xysin(y2)dy = 0, the integrating factor is O a. ex O b. 3x O c. x 3 Od. e-x

A: Let us consider the differential equation Mdx+Ndy=0 Find the integrating factor  Determine the…

Q: Use 2- step substitution St* sin (t5) cos(t5)dt

A: