f(x) = xe (1+e*)

Q: Find dy/dx by implicit differentiation   2x3 +x2y  -xy3  = 2

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Q: Find the relative extrema using both First and Second Partial Derivative test f(x) = Sin2x ; 0<x<n

A: i) The given function is fx=sin2x. Given that the domain of the function is 0,π. Obtain the first…

Q: Find the derivative: y = ln² (3x + 1) O y' = O O O y' = y' = y = 2 ln(3x + 1) (3x + 1) 6 (3x + 1) 3…

A: Consider the function y=ln2(3x+1). The objective is to find the derivative of the function.

Q: Find the derivative of f(x) = 3x° cos(x). 8 CoS f'(x)

A: Given query is to find the derivative of the function.

Q: A second derivative Findd2y/dx2 if x2 + y2 = 1.

A:

Q: Find the derivatives of the functions in Exercis y = xe-x + ex3

A: y=xe-x+ex3

Q: Find the first derivative: y= ln v5x3 –- 2 5, O y = 222 %3D 523-2 O y' = 322 5z3-2 O y' = 622 5z3-2…

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Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – /cos(x) At the point (, (2n…

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Q: Find the relative extrema of f(x) = 8+ 126x – 7x2 using both first and second derivative tests. f…

A: If second derivative is less than zero then there is relative maxima.

Q: Find the derivative of Ox²2cosx + 2xsin x O 2xcos x O x² sin x + 2xcos x O x2cosx y=x²sinx

A: We know that if f(x)=g(x)h(x) then  f'(x)=g'(x)h(x)+g(x)h'(x)

Q: Compute the derivative of y = ln ( – V1 – 2 cosh x (x° + 2) |

A: To compute the derivative of,  y=ln1-2 cosh x .x3+2x.x-1.

Q: Find the derivative of the function y = arctan x + x 1+x²

A: Given: y=arctanx+x1+x2Recall the formulas:ddxarctanx=11+x2     ..........1ddxuv=vdudx-udvdxv2…

Q: Find the derivative of the function. 2x F(x) = arctan(t) dt 1 2 arctan(2x) F'(x) = (arctan(Vx)) -

A: Here we have,

Q: What is the derivative of f(x)=3cos(x)+2sin(x) at the point x=−π

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Q: What is the first derivative of f(x) = ln 3z²+7z ?

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Q: What is the anti derivative of  f(x)= 2sin(x)-sec2(x)

A: Given information

Q: The total derivative of f(x,y) = ylnx  is

A:

Q: Find the relative extrema of f (x) = 7+ 144x – 9x? using both first %3D and second derivative tests.…

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Q: what is the differentiate of f(x)=ln x

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Q: Find the second derivative of f(x) = x2+ e* - COSX. O a. f(x) = 2x + xex - cosx O b. f'(x) = 2x + e*…

A: Solve by derivative

Q: 2) Let f(x) = x' +x² – 5x – 5. Use the second derivative test to classify the critical points.

A:

Q: 2.Find the derivative of y = In cosh x. %3D

A: Using chain rule of differentiation.

Q: Use the second derivative to find the location of all local extrema for f (x) = x + x2 – x3, -

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Q: Use central difference approximations to estimate the first and second derivatives of y = e* at x =…

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Q: find derivative of the U function 1-x f(x) = sec-1. 1+ x ーオ

A: Explanation of the answer is as follows

Q: Find the derivative of the function y= arctan x +x/1+x2

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Q: Find the indic ed derivative. dz x2 for z = x2 dx 1 - x - 2x2 dz dx

A: Formulas:

Q: The derivative of the function y = etan(4x) is: a) y' = tan (4x)etan(4x) b) y' = 4 sec²(4x) etan(4x)…

A: Given data: The given function is y=etan(4x). Differentiate the given expression with respect to x.…

Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – cos(x) 2n 4+v3 3' 23 At the…

A: Answer

Q: Find the derivative of x2cosx+2xsin x O 2xcos x O x² sin x + 2xcos x Ọ xzcosx y=x²sinx

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Q: Find the derivative. f(x) = x sinh(x) - 4 cosh(x) %3D f (x) =

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Q: FInd the derivative of f(x) =ln 1+ex/1-ex

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Q: Integrate xtanx with respect to x

A: We have to solve this integral by  Integration by parts rule, Formula is  ∫uvdx=u∫vdx-∫u'∫vdxdx

Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – /cos(x) (2n 4+V3 2V3 At the…

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Q: 2. Use central difference approximations to estimate the first and second derivatives of y = e* at x…

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Q: Find the critical value of f (x) = vx² + x – x using the second derivative test. %3D

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Q: N= cos(5x) (SX メコ

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Q: Find the relative extrema of f(x) = 4+70x – 5x² using both first and second derivative tests. f (x)…

A: Given:- f(x) =4+70x-5x2  To find:- Relative extrema of f(x) using both first and second derivative…

Q: Find the derivative of the function y = x tanh−1 x + ln√(1 − x2)

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Q: Find the linear approximation of the function f (x,y) = ln (x - 3y) at point (7,2).

A: To find the linear approximation of the function fx, y=lnx-3y at the point 7, 2.

Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – /cos(x) (2n 4+v3 3' 2v3 At the…

A: Given: f(x) = 1 + csc(x) -cos(x)   To determine: Equation  of the tangent line at the point…

Q: If f(x,y) is a real valued function of two variables then what is the second derivative of f?

A:

Q: Find dy/dx by implicit differentiation. 3+10xv+4x-5x=0

A: Given

Q: 2. tanh-'x + lny1 – x²

A: We have to find derivative

Q: nd derivative of f(x) = x In(x)

A: We have to find the second derivative of the given function

Q: Find the derivative of the function.

A: Given

Q: f(x)= sinx/cos x+1

A:

Q: Determine the n-th derivative fn) of the function f: (0, +0) → R, f(x) = x ' exp ( 1 - ), n EN

A: f(x)=1x,  f:(0, +∞)→R,…

Q: Find the critical numbers of the function and apply the First Derivative Test to identify all…

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Q: Find the derivative. f(x) = tanh(2 + e4x) f '(x)

A: