Let z=In(x²+y²) where x=ue"sin t and y = ue"cos t. If u=- 2 and 1=0 then is equal to %3D ....

Q: 1- Calculate the value of y if: a-y= sin "(0.25) + sinh (2). b- y= sinh (15)+cosh"(31)

A: Note: According to our guideline, we will answer one question. As the exact one is not specified.…

Q: Determine 1 dx , 4x2 +1 (i) (ii) x cos x dx .

A: Determine.  (i).  ∫14x2+1dx             ⇒∫14x2+1dx=14∫1x2+14dx  ⇒∫14x2+1dx=14∫1x2+122dx…

Q: Find y" for the following function. y = 5 sin x cos x y" =|

A: We will find y'' as following.

Q: 4. Find d?y/dx² for the following functions: b) y = cos*(sec² 3x)

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Q: Evaluate each of the following: (a) /" In(x) dx

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Q: Find y" for the following function. y = 4 cos x sin x y" = У'-‑

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Q: -. Solve for dy/dx a. y = *+ sinx cos x † Sin X

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Q: 7. Let y = tan (3x - 2), find y'.

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Q: -(sin(xyz)) = O xô zô y

A: Partial differentiation of the function with respect to x means to differentiate the function only…

Q: Find the second derivative of y = 6xcosx.

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Q: Find y" if cos y + X =y

A: Given, cosy+x=y We have to find y''.

Q: Use implicit differentiation to find dy/dx. e3x = sin(x + 8y) %3D Select one: O A. dy -3eX %3D dx…

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Q: 2. Differentiate. f(t) = et sin(2t)

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Q: Find if z = sin(uv)cos(uv), where u = e' and y = e2t. dt %D Lütfen birini seçin: O A. 3e(sin2(e3t) -…

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Q: 2. Integrate | sin x cos? x dx

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Q: For | cos 3x cos 4x dx :

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Q: 1. Find dx dy for the following functions: 1) y = (x- 3)(1- x) (ans.:4 - 2x) b (ans. :-,) x* 2) y=…

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Q: Find y' and y". . sin3y=x²+tany+1

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Q: 3. Show that: • T/2 sin" x dx • T/2 cos" x dx

A: Recall the property of definite integral:

Q: Let f(x) = e cosx, sx %3D 2. Express your answers in exact form. ElN

A: Inflection point occurs when the second derivative of the function equals to zero.

Q: x2 tan In y

A: Here we can find dy/dx as below