Find f"(x) for the functions x² +5x f(x) = ex b. f(x) = (x² – 1)e* a.

Q: i. y= ) In (x+3

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Q: Find the differential of the function: y = x In x

A: Solution:Giveny=x ln xTo find the diffferentiationformula:(uv)'=uv'+vu'ddxxn=nxn-1ddxln x=1x

Q: find (y') by Implicit differentiation e(2x+3y) = x² – In(xy³) 1 Add file

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Q: Find the first derivative of y = e3x. 3e3x

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Q: What is the critical point of the function f (x) = cos x?

A: what is the critical point of f(x)=cos(x)? for critical point, f'(x)=0

Q: Find y" by implicit differentiation. x² + 4y² = 4

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Q: Find the derivative of: 9e 7sin ( 3x*) Use e^x for e". -

A: We use chain rule to find the derivative.

Q: 3. Find the derivative of the function. y = In(t2) – arctan(-

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Q: 'the line tangent to the graph of y= In(3x) + 2x e at x=1 6 Jx-1 by using quotient rule. Vx +1 for…

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Q: The derivative of f(x) = 5x – Vx + (sin)x – e² -

A: Given; f(x)=5x4-x1/3+[sin(π/2)]x-e2

Q: use the Chain Rule to find the derivative. y = cos3(e4θ )

A: Given: The function given is  y=cos3(e4θ)   To determine: The derivative of the function y=cos3(e4θ)…

Q: Find the differential of the function y=√x3+4x at x=2.

A: Given the function:

Q: x + x dx x2

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Q: Calculate differential: f (x) = = e-* cos(3x) + 2 of the range [1,2] with h=0.05 a) Using the…

A: Equation is f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of the…

Q: Find the differential d8y of the function y=exsinx.

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Q: Find the derivative of y with respect to x. 2. y²(x + 2y) = e²

A: Given,

Q: 2x2+x dx x+1

A: Integration ∫2x2+xx+1dx

Q: 10. S(2x – 3) dx e 2x2 - ебх

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Q: Find the derivative of f (x) = Ln e*+1 using the limit process. %3D

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Q: Use the Chain Rule to find the derivative. y = cos3(e4θ )

A: We have given y=cos3e4θ Then, dydθ=dcos3e4θdθ=3cos2e4θ-sine4θ4e4θ=-12e4θsine4θcos2e4θ

Q: Find the linear approximation of f(x)=ln(x) x=1 and use it to estimate ln(1.1). L(x)= ln(1.1)=

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Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate ln(1.33).

A: The linear approximation of f(x) at x=a is given by L(x)=f(a)+f'(a)(x−a) Given, f(x)=ln(x) at x=1.…

Q: Find the nth-order differential of the function y=2x.

A: To find nth order differential of the given function.

Q: determine dy/dx of the implicit function: 2x2y-sinxy2+e-xy=10

A: Given implicit function is  2x2y-sinxy2+e-xy=10 To find: dydx

Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x*+1) 3- xy + x²y = 3 at x = 1 4-…

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Q: Find the differential of the function y=xxe2x at the point x=1.

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Q: Shows the derivative function of: u³ + 2u, where u = x² + 3

A: Let's find.

Q: Let y = x(ln x)² – 2x In x. Find the value of X for which the second derivative, y" (x), equals…

A: Solve the following

Q: Find the derivative: 1+ e2x = cos 1 - e6x f(x) f'(x) =

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Q: Find the differential of the function. u = 2x +

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Q: Find the derivatives of: d/dx (ex-e-x/ex-e-x) And the derivatives of: f(x)=ln((2x+1)3/(3x-1)4)

A: the given expressions is: dex-e-xex-e-xdx the given function is: f(x)=ln2x+133x-14

Q: Find the first And 2nd derivative  F(x)= e^x sin4x

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Q: Find the interval in which function f(x)=sin (log,x)+cos(log,x) is decreasing

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Q: Find the derivative of the function  f(x)= e^-3x ln x

A: Given function is

Q: (a) By using the chain rule and the derivative = (xl) if x>0 (-1, if x< O' dx find - (Ix – x|)DvxE…

A: Given : ddx(x)=1 ,     if x&gt;0-1 , if x&lt;0 To find : ddx(x3-x) , where x∈(-1,1) and x≠0

Q: Find the 10th-order derivative of the function y=(x2+4x+1)√ex at the point x=0.

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Q: (a) By using the chain rule and the derivative if x>0 (1, -1, if x< O' d (\xl) = dx | d find - (lx3…

A: Just break the mod function in two parts and easily calculate the derivative.

Q: Y= In (In2 (1-x))re?

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Q: Find the second differential of the function y=x2cos2x.

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Q: Find the derivative: f(x) = cos 1 + e8x 1- e6x – ebz f'(x) =

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Q: Find the derivative of y with respect to x if y = (5x2 – 10x + 10) e - 6x y' =

A: We have to find the derivative of y with respect to x.

Q: Find the linear approximation of f(x)=ln x at x=1 and use it to estimate ln(1.24). L(x)=?…

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Q: Find dy by dx when  f(x) =2x²-x+5÷3x+2

A: The derivative of a function gives the rate of change of a function when an infinitesimal change is…

Q: 3. Find the derivative D(x *arctan(x)) And the integral 6x dx 9+x

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Q: 3 +Ve³ .2 3x e: f(x) =

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Q: Find the linear approximation of f(x)=lnx at x=1and use it to estimate ln⁡(1.3) L(x)=? ln 1.3≈?

A: First find the linear equation at x=1  then find the approximate values

Q: Find the derivative of f (x) =arcoth (e³" ).

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Q: Find the derivative of the function: y = In e+2*+1 Oy = x"[(2x(ln x + 1) + 1] y = x*(2 + x + x² In…

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Q: Find the first derivative of x² + 3xy + y3 = 10 implicitly.

A: The given function x2+3xy+y3=10

Q: Find the first derivative 1. y = In v4-x2 %3D 2. In(x2 + y2) + 4arctan = 5 y %3D dy x+4 3. Find , if…

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