Find the average rate of change of the function f(x) = - 2x – 7x + 8, over the interval [-1,1]. - 2x?

Q: Find the derivative of the function f(x.y) =x² +xy +y° at the point (7,8) in the direction in which…

A: Introduction: For a multi-valued function, the gradient is the vector that is directed towards the…

Q: Find the derivative of the function f (x, y) = x²y + y²z: at Po(1,2,3) in the direction of û = 2î –…

A: To find the derivative of the function f(x,y)=x2y+y2z at P0(1,2,3) in the direction of…

Q: Use differentials to approximate the change in y = f(x) from x = 4 to x = 4.1 for the function, f(x)…

A: It is given that,

Q: Find the derivative of the function. f(x) = In(x + V7 + x²) f '(x) =

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Q: Find the derivative of the function f(x) = e(z²-3z).

A: The given exponential function has one independent variable which is x.

Q: Find the derivative of the function at P in the direction of A g(x, y) = x - (v² /x)+ /3 sec*(2xy),…

A: To find: The derivative of the function at P0=1,1 in the direction of  A=12i+5j Given information:…

Q: Consider the function f(x, y) = y³ – 2y – x². Find the direc- tion of greatest increase at the point…

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Q: find the derivative of the function at P0 in the direction of u. ƒ(x, y) = 2x2 + y2, P0(-1, 1), u =…

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

A: Given the function:

Q: Calculate the differential of the function y=x5−7x3+5x at the point x=2 when dx=0,2.

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Q: Find the derivative of the function f(x, y) =x2 + xy+ y at the point (-5,-4) in the direction in…

A: The function is given as , fx,y=x2+xy+y2 find the derivative at point -5,-4 in the direction in…

Q: What is the derivative of y = V(x? V(a2 – 1) (x + 1) ? -

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Q: Solve for the 2"nd derivative of the function f (x) = 3x5 – 4x3 + 7x² – 10. a. 15x* – 12x2 + 14x b.…

A: Given: fx=3x5-4x3+7x2-10 To Find: 2nd derivative of the given function

Q: 2. Given: y = f (x) = (2x-2 + 5x³). What is the slope (gradient) of the first derivative function at…

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Q: Use the second derivative test to find the local extrema for the function f(x,y) = x² +y³ + 2xy – 3x…

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Q: 3. If f(r, y) = x*y - 2x-4y, then the total derivative of f

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Q: 2. Find the derivative of the function f(x, y) = 2x² – y² at the point M = (1,1) in the direction…

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Q: Find the relative extrema using both the first and second derivative tests. f(r) = 2x³ – 9x² + 12x.…

A: Consider: fx=2x3-9x2+12x. Critical point is the point where the derivative of the function is either…

Q: Given the function f(x) = (x-2)2 + (y-3)2 (i) Find the critical points. (ii) Using the second…

A: The given function is: f(x,y)=(x-2)2+(y-3)2

Q: Find the second derivative. 1 h(x) = x2 %3D | h"(x) = %3D

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Q: Calculate the differential of the function y=2x x2−3 at the point x=3 when dx=−315.

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Q: Use the second derivative test to find the local extrema of the function f(x, y) = x+ 2xy – 6x –…

A: Step 1: Find the partial derivativesfx and fy and put both equal to zero and we getcritical points…

Q: 4 Find the derivative of the function y= f(x)= Jx(x-8). %3D

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Q: What is the instantaneous rate of change of f(x) = V +2-3 at %3D x = -2?

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Q: Q. / Find the derivative of y = (In(x²))'n(x²).

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Q: Find the derivative of the function at P, in the direction of A g(x,v) = x - (y² /x)+ V3 sec (2xy),…

A: Given that  g(x,y)=x-y^2/x+√3arcsec(2xy) P(1,1) and A=12i+5j To find the directional derivative of g

Q: Find the derivative of the function. x3 y -1 -2x3+3x2 y's (x- 1)2 y'= 2x-3x2 (x-1)2 y'= 2x3+ 332 (x-…

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Q: The derivative of the function y = x² In(x + 1) is:

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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 linear fractional function y=ax+bcx+d.

A: We have to find the derivative of    y=ax+bcx+d ddxy=ddxax+bcx+dWe have to apply division rule…

Q: Find the second derivative f"(x) for f(r) = e(z+2)*.

A: Given: fx=ex+24 for finding second derivative of given function we first take log and find first…

Q: Using the definition, find the derivative of fz) = 3 z^-6 z² at point z= 0

A: Given,          fz=3z4-6z2

Q: Find the derivative of the function. 2 f(x) = 3F + 3cos x V X

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Q: Find the derivative of the function at the given point in the direction of A. f(x.y) = 6x+10y,…

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Q: Find the derivative of the function f(x) = V (x² – 2)* at x = 1.

A: Given f(x)=(x2-2)23      ⇒f(x)=x2-2213⇒f(x)=x2-223

Q: find the second derivative of y = x In x A 1/x в) 1/2х D) 2x

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Q: Find the differential of the function.

A: Differentials are infinitely small quantities. We usually write differentials dx, dy, dt (and so…

Q: The total derivative of f(x,y )=3 x+ 3 y-41n y is

A: Given function is fx,y=3x3+3y2-4 ln y find the total derivative  dz=fxx,ydx+fyx,ydy

Q: Find the first derivative. (a) y=x* (b) y =xnx 2.

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Q: Find the derivative of the function f(x,y) = tan at the point (3, - 3) in the direction in which the…

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Q: C. Apply the chain rule to find the derivative 1. y = (8 - 3x )3 3. y = (1-x)7 2. y = V2x + 1

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

A: We are asked to find the derivatives of the function using limiting process.

Q: Q11) For the z= (2x+3y)10,which is correct ?partial derivative

A: Given,  z = (2x + 3y)10 To find the partial derivatives.

Q: Find any relative extrema. Where applicable, use the Second Derivative Test to verify. (a) f(x) = (x…

A: a)  f(x)= (x+9)2 b)   f(x)= x4 -2x2 +6 c)  f(x) = 2x +18/x          provided x≠0 To find relative…

Q: a) Find the derivative of the function: T+ V3x f (x): 3x-1

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

Q: Find the derivative of the function. f(x) = /7+ V5+ VI f '(x) = %3D

A:

Q: find the derivative of the function at P0 in thedirection of v. ƒ(x, y) = 2x2 + y2, P0(-1, 1), v =…

A: Given: fx,y=2x2+y2  We know that, The direction of v is the unit vector obtained by dividing v by…

Q: Find the derivative of the function at the given point in the direction of A. f(x.y) = 7x + 8y.…

A: Directional derivative: - The partial derivatives of f give the slopes ∂f∂x in the positive…

Q: Find the derivative of the function. f(x) = /2 + V1+ Va f (x) = ||

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Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of df-1 at x = 1. dx

A: We have given function;