Eliminate the arbitrary constants of    y= Ae^(5x) + Bxe^(5x) + e^(3x) (Ccos10x + Dsin10x)    Where A, B, C, and D are the arbitrary constants

Q: Find the 3rd derivative of the function y = (3x³ – 7x2 +5) (x²+5) O y" = 120z2 - 168z + 90 %3D O g"…

A: Recall:Firstly product the givern term and find function of 'x'   i.e;   y=fxSome formula:∙ddx…

Q: An equation of the tangent line to the curve y= 4x2-8x-5 at the point (-1, 5) is O y14x-9 Oy 14x71 O…

A: The curve is given by,

Q: y = 2 ||

A: We have to find the derivative of the function y = 1-x2ex2

Q: what would be the output if the 2nd derivative is negative

A: We know that for a function y = f(x), the points of extremum are obtained if the first derivative of…

Q: Find the derivative. y= In x+3 %3D

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Q: Find the third derivative of y = (6x - 1). Show your %3D in negative exponent.

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Q: Use central difference method to estimate the 1st derivative of the following function at x = 2 and…

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Q: Verify the statement by showing that the derivative of the right side equals the integrand on the…

A: To calculate the integral

Q: at the point (2, –1). Find the maximum rate of change of f(x,y): x2 + Y

A: For maximum rate of change we need to calculate magnitude of gradient bat point (2,-1)

Q: What is the slope of the tangent line to the graph of the solution of y' = 5√y + 3x³ that passes…

A: As we know that; The slope of the tangent line to the given curve is equal to the derivative of the…

Q: Find the derative: yain Jx2+4x+1 derivative.

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Q: y=C1x + C2e + x2

A: The givne equation is:y=C1x+C2e-x+x2To eliminate the arbitrary constant/s

Q: find the derivativey=log(to the 4th) time (2x Third -6x)

A: To apply the rules for derivative of composite functions

Q: 5 Calculate the second and the third derivative of y = 6x – y": y"

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Q: Find the tangent lines. To the cubic y=x³-2x+3 parallel to the line 10x-y=3

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Q: Find the derivatives of the functions in Exercis

A: We need to find the derivative of the function, y=5-2x-3+182x+14

Q: LY 5- -4 2- -5 -4 -3 -2 -14 -2+ -3

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Q: Find the derivative of: y? – 4x = 0 at point (4,4)

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Q: Find the slope of the line tangent to 2xy + π sin y = 2π through the point (1, π/2).

A: The slope of the line tangent to 2xy+πsin y=2π through the point 1,π2.

Q: maximum point of y x – 2

A: Condition for Extreme Value: A continuous function fx, y has extrema at a, b if fx=fy=0 at a, b…

Q: Find the derivatives of the functions in Exercis

A: Given, y=5-2x-3+182x+14

Q: Question 3

A: Consider implicit equation and

Q: If 4x + 4x + ry = 3 and y(3) = 15, find y'(3) by implicit differentiation.

A: We have to find derivative at that point

Q: 3. = 2x-y х+3у

A: We will differentiate the given problem with respect to x.

Q: Ax) = (5x* - 3x)(2x° – 7x) en x =

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Q: Determine the derivative of y. アミeV10x+5

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Q: Find two positive numbers whose product is 750 and for which the sum of one and 10 times the other…

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Q: calculate the derivative y = ecosh−1 x

A: Given The chain rule of derivative is given by: The derivative of the inverse hyperbolic function…

Q: Find both first partial derivatives. az

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Q: Find the slope of the line tangent to the graph of x2+2xy2+3y=31 at th epoint (2, -3)

A: To determine the slope of the tangent at the point (2, -3).

Q: Derive a formula that approximates the second derivative of the function sampled at x = 0, 0.01,…

A: Let us assume that second derivative function  f"x0=Afx0+Bfx0-h+Cfx0+2h can be rewritten as…

Q: Determine the second derivative of 2x+ y-- 4 y 6.x (y + 2)--9(y+2) A B - 6x (y+ 2)-+ (y + 2) - 6x (y…

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Q: What is the value of the second derivative y" at the point (4,3)

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Q: Find the equation of the tangent and the nirmal to the curve y=5x4 at the point (1,5)

A: Given curve,  y = 5x4  To find the equation of tangent and normal at the point (1, 5)

Q: x2/3 - y2/3 -y=1 ;(1, -1)

A: firstly we find the slope(m) by differentiate w.r.t. x  and then put the slope in equation of tanget…

Q: find tangent line to the curve y=3x/7-x at a point of (-3,2/7)

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Q: Find the slope of the tangent line to the graph of x4 + 5xy - 12x + 11 = dt at the point (1 , 0) on…

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Q: Find the first and second order derivative w=3z7-7z3+21z2

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Q: Determine the derivative of y. y = eV14x+6 %3D

A: Please refer the attached image for complete solution.

Q: Find the second derivative of y = -5 %3D -

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Q: Explain how to find a first partial derivative of a function oftwo variables.

A: To get the first partial derivative of a function z = f(x, y) with respect to x we have to…

Q: Find the slope of tangent line for the equation x^2+y^2=5 on (1,2)

A: The given equation of the line is,

Q: 5z²)* 4/3 %3D

A: (3). The function is given by Hz = 1-5z243 To evaluate: The derivative of the function.

Q: ength of the curve 1 1 < x < 2. 6 10x3 +

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Q: Find 1" and 2nd order partial derivative for the function ax²+by²+2hxy and also verify дхду дудх

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Q: Determine the second derivative of 6 y – xy²= I Ay"= 2y³ ( 6 – 2x y)-2 ( 2 - x y ( 6 – 2x y )-1) ®…

A: Let's find.

Q: Calculate the second and the third derivative of y = 5x- 9 y": y"

A: Using derivatives rule &amp; formula.

Q: Find the derivative of the function at Po in the direction of A. txу) - - ху + у, Р,(10, - 2),…

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