( w"-y+ (x+ ¥)'y = In (금 + z) y(-}) = 1, y' (-}) = o %3D

Q: find f(x) so that f'(x)=-4e^(x)-6sinx

A: To find f(x) from f'(x) , we have to integrate f'(x) We first separate the integral

Q: y = (x+1)arccsc(x²) .2'

A: Given: y=x+1csc-1x2 Product rule of differentiation states, ddxuv=v·ddxu+u·ddxv Differentiating the…

Q: d. yy'- y = 6 e*, y(0) = 1 %3D е. %3D %3D

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Q: find d2y/dx2 at x=2 a. y=x^(2) (\sqrt(x)+2) b. y=3x^(2)-(4)/(\sqrt(x))

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Q: Find f. - Vi- () -- 8. f'(x) = 9 %3D V1-x2 f(x)

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Q: s(t) = 1/t^3;  (-6 , -1/216) s'(6)= ?

A: Given: s(t)=1t3−6<t<−1216s'(6)=?

Q: If h'(3) -1 and h'(1) = 5, then |h"(z)dr = %3D %3D (A) -6 (B) 4 (C) 5 (D) 6 (E) 9

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Q: Find y' and y". In(2x) y = 1- In(32) y' y"

A: The given function y = ln(2x)/(x^5):   Find the first derivative of the function y = ln(2x)/(x^5)…

Q: Ex+ 8x3-72x?+4 三X'

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Q: if y= (1+e^x)X^3 then find y`

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Q: If y = Vcot3tan³seccscx² find y' %3D

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Q: 3. y' = 3x? –2; y(1) = 5

A: When the linear differential equation is in the form, dydx+py=Q    ..........1 Then the solution of…

Q: Find A^ if A :

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Q: Calculate y'  if y=1/(x+(x)^1/2))^1/3

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Q: If h'(3) = 5 and h'(1) =-1, then h"(x)dz %3D (A) -6 (B) 4 (C) 5 (D) 6

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Q: Exercise 1. Find 뿐 for y =DIn (골) (1A) + 3극 3z-2 z(r-1) (1B) 분 (1C) -= (1D) 를-3금 z-1-r z(1-1) (1E)…

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Q: 9/ (4x’y² - 2xy)dx + (3xʻy* - x*)dy = o

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Q: C) = ("; ')-(,",) n Q1. Show that : r

A: R.H.S;=n+1r-nr-1=(n+1)!r! (n+1-r)!-n!(r-1)! (n-r+1)!=1 (n+1-r)!(n+1) n!r(r-1)!-n!(r-1)!=n!…

Q: Differentiate. y = 1 — х* y' =

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Q: y" - y' - 2y= e* %3D

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Q: Evaluate y''' or d^3y/dx^3 of the function (1/3)x^3 + (1/3)y^3 = (1/3)^2  when x = 0

A: Given, 13x3+13y3=132.   The objective is to find y''' at x=0.   Now, 13x3+13y3=132y=91-3x333

Q: Calculate y', y" and y" for y = . [Hint: y= r-le", product rule, several times.] use

A: Topic  - differentiation by parts

Q: Find g'(x) if g(x) %3D Зx е бх

A: Product rule of the derivative is, (uv)’=u’v+uv’ where u and v are the functions of x.

Q: a) If h(u)=-9e^(5u)^(4), then h'(u)= b) If F(x)=e^(4x^2+5x), then F'(x)=

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Q: 2y''' - 3y'' - 3y' +2y =(e^x + e^-x)^2

A: We have to solve the differential equation  For which we first solve the homogeneous equation and…

Q: 5. (y" – y) = e-X cos(3x) %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: solve. y'−( 1/x) y = x^3, where x>0

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.