2. f(x) = x 3 - 10x 12 = 0 a.

Q: Suppose that x and y are related by the equation Proportionality 1 dt. Vi + 4t² |Show that d²yldx²…

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Q: (c) | Vtan(x) sec (x)dx 3

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Q: -S² √√x" dx -2- ។ (X) 5 JX dx -2

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Q: 9. Find the first derivative: f(x) = 3ex %3D x2 (x+1)

A: Derivative of function

Q: 8. the second derivative of f(x) =3e^5x , is а. 15е^5х b. 125e^5x с. Зе^5x d. none of the other…

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Q: Compute the indicated derivative. d + 7x)(x2. dx x = 2

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Q: 9. If | f(x) dx = 20 and f(x) dx = 3.6, find f(x) dx.

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Q: 18 The derivative of the function f(x) = x² + is 18 4x3 + (æ³) 18 O 4x³ - (æ²) 18 4x° + (x) 4x + 18…

A: d/dx(xn)=nxn-1 Given f(x)=x4+18/x  To find the derivative of f(x) differentiate once

Q: What is the first derivative with respect to x of f(x) = (x² – 4) (3x – 2)? a. (2x)(3) b. 6х (x + 2)…

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Q: 4. Write the equation of the line tangent to f(x) = (e* +2x +1)In(e* +2x+1), when x = 0.

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Q: Find the second derivative [ f"(x)] of the given function: f(x) = eln Vx²+2 %3D (x2 + 2)) x(x² + 2)-…

A: Given problem:- Find the second derivative [f''(x)] of the given function:   f(x) = eln√(x^2+2)

Q: 18. S V1+x dx 1-х

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Q: 10. Find the derivative of y = V3x + 2. c) d) 3x a) 2V3x+2

A: Using derivatives

Q: Example 3: Estimate S, x² dx with n=4 by Midpoint Method. Solution:

A: Here first we will divide the integral range into 4 equal parts and then we will calculate the…

Q: -2x y" + (e by = 0 (e-* = z) -

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Q: 5. ft² √1-1³ dt 6. J (2x+3) dx (x²+3x-6)⁹

A: Given 5. ∫t21-t33dt6. ∫2x+3dxx2+3x-69

Q: (2+3t2 3x2 dx 1+ x3 6. Find the derivative of the function F(t) = 2-3t2

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Q: Use variation of parameters to find the general solution: x^2y''+xy'-y = ln (x)

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Q: d’y - 2 y = 5x' + In(x²). dx

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Q: 7. f(x) = sech"(vi-x) 8. y = sech Inx

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Q: What is the derivative of the function f(x)= In(3x2) ? а. f'(x)= 2 b. None of these. с. 1 f'(x)= %3D…

A: We have given that  The function is f(x) = ln(3x2)

Q: Find the fourth derivative of ƒ (z) = 4z" f(4) (z) =

A: We can make it easier for you

Q: 13. In y = what is the derivative of 2x2 +3? x+1 a) 2x b) 4x c) 4x +3 d) 7

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Q: In (xv/x² + 7). n (xVx2 %3D · Find the derivative of the function y = In

A: To find the derivative of the Given function, we have to apply chain rule and product rule.

Q: 27. The first derivative of y = is (4x+1) -24 b. 24 C. -6 6. (4x + 1)+ (4x + 1)+ (4x + 1)4 (4x + 1)*…

A: y=-2(4x+1)3

Q: 5. y = x3 – x²Cos(x)+ 2xSin(x) + 2Cos(x) -

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Q: Q:1 Find the second derivative of f(x) = 2x5 - 3VX7 at x = 1 rounded to five decimal places.

A: To find the second derivative of  f(x)=2x⁵-3x7/3 at x=1

Q: 10. x = Vt-2, d²y y =t2-3' dx2

A: The given question is taken from the derivative and we have to find the derivative of the parametric…

Q: Integrate x2 e a) S- 2x -d.x 2 b) S- -

A: By using integration property, we calculate the following Integral.

Q: So(VE + vZ)° dx = f° xdx - (Vã + vZ)dx • f;(Vã + v2)dx 6. So x(x² + 1)dx = - S x*dx + f, xdx 7. S'…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 15) 4S(5x)] = x² , then f'(x) = ? %3D dx

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Q: Find the second derivative of y = Vx² +x-3 O 6/x O 12/x^5 O 6/x^2 O 12/x^3

A: dxndx =n.xn-1 dcdx =0 ; where, 'c' is an constant number.

Q: 2 If "IF(x)dx=6 and frox)dx=7.50mm [rodr then f(x) dx = 5

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Q: 3. fz √z dz 4. (2x² 3x + 5) dx -

A: 3. ∫zzdz4. ∫2x2-3x+5dx

Q: Find the derivative for x 1 1. (4Tx)"/2 e 4t |t|2 e 4x 2. 3.

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Q: 1. Find the derivative of the following f) y = (2x − 1) ( x³ − x) + √x[2(x³ − x) + (2x − 1)(3x² −…

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Q: In (4x+7) 1. Find the derivative of f(x) 5x e 10-18 x? Evaluate the integral: 5x-3x 5 6x*-3x?…

A: Please see the explanation below

Q: 10. Solve for the derivative of y IMPLICITLY 22 + Væ³ + 2y= y²

A: Note: According to our expert guidelines only first individual question is to be answered, kindly…

Q: By differentiating x² – y² = 1 implicitly, show that d²y | dx² ||

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Q: 1,- X73X+2 dx (x+リ) Izafhinx dx Ax. Iォfュース alx dx X43X+2 X+1

A: Since, you have posted multiple, we will solve only first part. If you want solution of other…

Q: 2. The derivative of y = (1 + Vx3) (x3 -2 V) is y'=-3x4-3xs-2z2-11xº.

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: 2. Find the derivative of (a) f(x) = x* + 4x 2 + 4e" (b) f(x) = 2 tan (x) – 6"

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Q: Differentiate the functions: 1. y = 3x – Vx 2. y = 2 – 3x – 3. Given the function f(x) = x³ – 5x +…

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Q: 3) Find d²y/dx² at the point (1, 1), if x6 + y6 = 2.

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Q: 10 The derivative of the function f(x) = x7 + - 10 726 + (r³) 10 71° + (2) 1 10 7x + 10 10 726 (z²)…

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Q: Vaz x² S. (2) dy dx

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Q: What is the derivative of y = (2x)" O (2x)^(x) (1-In2x) (2x)^(x) (1+2 In2x) (2x)^(x) (1+In2x) O…

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