nd the derivative of the functionf(x) = v 5x+6 using the limiting proces A) S'x)= - 2 5x+6 Sx) = 2 5x+6 B 5x f'x) = - 5x+6

Q: Find the derivative using the theorems on derivatives. dx x2-2 1 y = 2.y = (x² – 1)³(x² + 3)² x3+4x…

A: Given functions to be differentiate are    1.   y=x2-2x3+4x    3.  y=x2-2x      we will make use…

Q: Find the direction derivative of f(x, y, z) = x²y -zx -yx point (1,-1,1) in the direction 3i+4k x at…

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Q: 4. It f(x,)= (x?+Zy^)+Z and ū= a.) Find the derivative of t in the direction Of ū at 13,2) -

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Q: Find the derivative of arctan(x² + 1) -2x O f' (x) = -2a2 – a4 2x f' (æ) = x² +2 2x f' (x) x4+2x²+2…

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Q: When the Second Derivative Test Fails Analyze the critical points off (x, y) = 3xy 2 - x 3 .

A: Given Data The function is f(x,y)=3xy²-xᶟ.   Differentiate the function f(x,y)=3xy²-xᶟ with respect…

Q: Find the derivative of the function. rsin(x) y = In(1 + 5v) dv y'(x) = sin x In(1+5 cos x) + cos x…

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Q: Consider f(x, y) =(ax² + by²). Based on the second derivative test, what are the conditions…

A: Answer

Q: 2. Calculate the first derivative of f using the forward and backward difference approach in the…

A: The objective is to calculate the first derivative of f using the forward and backward difference…

Q: he first derivative of y = 3x ++ 2V - a is %3D 3 10 y' 5 5z 5 3z 3 3 O y' 10 %3D 2V14 3 O y' 3. 10…

A: To find the derivative of: y=3x15-23x+35+2x34-5x23⇒y=3x15-23x+35+2x34-5x-23...(1) Note that:…

Q: ,2x Calculate the second derivatives of function f(x) = sin(x) + Ide²x at point x = 0.625 using…

A: Three point central differential formula for 2nd derivative   f′′(x)= f(x-h)-2f(x)+f(x+h)h2 Five…

Q: The derivative of y= sech-(Inx)+e sinh- (3x) equals Select one: +3esinh (3x) cosh(3x) y' = xlnxv…

A: The derivative of y=sech-1(lnx)+esinh-1(3x) is to be calculated by chain rule. The derivative of…

Q: Consider the following information fz(x, y) = 2xy - 2r³ and f₁(x, y) = x² + y² – 6. Use the Second…

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Q: A curve y = f(x) have length of the curve from x = 0 to x = 1/2. dy Vcos(2x – 2) as its first…

A: We have to find

Q: Compute the first derivative of y = 2x^4 - 6x^3 - 12x - 8 at the point x=0 based on the value at xo…

A: Five point FD Approximation and CD Approximation:--- ..  I this Error is 0%

Q: Determine the first derivative of the ff. function a. y = 400(2)**3 sin 3x b. y = Vxe2* cos x…

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Q: The directional derivative of f(x, y) = ln(xy) + x² at the point (-1,1) in the direction of from the…

A: We have to find the directional derivative.

Q: Compute the indicated derivative using the chain rule. X = 4 + 3t, y = -7t; Oy

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Q: Find all the critical points of f(2z, v) = - . 1 + 4x – xy? and classify them using the second…

A: The given function is;  f(x)=-x3/3 +4x -xy2.

Q: 6. Differentiate: a. f(x) In (In (3x)) b. Find equation of the tangent line to the graph of y-e³x.…

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Q: The derivative of y = 3cos(8x+6) is: 1. y' = 24 sin (8x+6) 2. y' = -24 sin (8x+6) 3. y' = -24 cos…

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Q: Use forward, backward and central difference approximations to estimate the first derivative of:…

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Q: 2.Evaluate the total derivative of u with respect to x for u = 6x²+4y² + 4z² when y = cosx and z =…

A: We have to find total derivative of u with respect to 'x'    where     u = 6 x2 + 4 y2 + 4 z2  Given…

Q: If we are getting the partial derivative of f(x,y) with respect to x, we are letting the y variable…

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Q: Compute the derivative: 4 te* dt d 3z2 L tet dz -1

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Q: Find the derivative of f (x ) =V sech( In (8x + 1)) - sech(In(8x + 1)) tanh( In(8x + 1)) A 2/ sech(…

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Q: 1. Find the directional derivative of the scalar function f = yzx^2 + 4xz^2 at the point P(1,-2,-1)…

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Q: 3. Verify the statement by showing that the derivative of the right side is equal to the integrand…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: The temperature in degrees centigrade (°C) at each point (x, y) on a curve 2x + y = 3 is given by…

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Q: The derivative of y= sech1(Inx)+esinh(3x) equals Select one: 1 3e sinh"(3x) O y' = - xInx/1-Inx…

A: Proceed as shown below...

Q: For a function f (x, y), (0, 0) and (1, 1) are two critical points. Also, fxx = 2x², fyy = y²2 and…

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Q: The population of a city is associated by the function P(x,y,z)=x² + 2y² + 2z². If the population of…

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Q: Find dy/dx using appropriate derivative rules. 1. y = 8x^5/2 - 7x-9 + square root of 5 2. ) y =…

A: Since you have asked multiple questions in a single request, we will be answering only the first…

Q: B) Find the derivative of the foiiowing: 1) y = 2sin2(5x) ,2) y = x, 3) xsin-14y = y tan-14x 4) y =…

A: As per the company  guidelines we have to solv first 3 subparts if suborats are not mentioned  So…

Q: Use Quotient Rule to find the derivative. x² + x - 2 3x +1: dy 2x+1 A. dx 3x + 1 dy B.…

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Q: Find partial derivative af for the function f(x,y) given below exp 2x. siny .(at the point (In2, 0

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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 derivative, g' (x) for the function 1 t -dt 1+t3 g(x) = 3z+2 9z+6 1+(3z+2) (1+(3z+2)*)-…

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Q: The second derivative y" of y = x3 + ex – sin(2x) is . 1. O y" = 6x + eX – 8 sin(2x) 2. O y" = 3x +…

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Q: Find the derivative of f(x) = 2x(sinx)cos(x) ? a. f(x)=sin2x+2xcos2x b. f(x)=2sin2x+2xcos2x c.…

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Q: Find the particular antiderivative of the derivative f'(x) = 3 -+x that satisfies the condition f…

A: Follow the procedure given below.

Q: Use Richardson extrapolation to estimate the first derivative of y = cos x at x = π/ 4 using step…

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Q: The derivative of y=esinh/x + coshVx equals Select one: 1 1 (esinh/cosh/x + Vx² -1 2х 1 O y' = e…

A: We have to solve

Q: Find the derivative. 3t cos (t) dt %3D O 3x cos (x4) O &va cos (x4) O 3 cos (x4) - 3x sin (x4) O cos…

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Q: Find the derivatives of the f: 1. y: sin (x²+3) 6. y= e tan 3x 7. y: e 2. y= tan (4x*) cot (3x-8) 3.…

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Q: Find the fourth derivative of f (z) = 27 + In (z) – 160z. %3D

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Q: 3. Verify the statement by showing that the derivative of the right side is equal to the integrand…

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Q: Find the derivative of the function. 11) y = cos x4 A) dy -4 sin x 4 B) dY - sin x4 dx C) dy - -4x4…

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Q: Find the maximum directional derivative of the function f(x.y) = x In y + x2y2 at the point (-1,1).…

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