(2) Evaluate the rate of change of i with respect to t when i 15t sin 3t and t=0.1. 2e" sin 2t when t= 0.5. 31 (3) Find the gradient of the curve z =

Q: a. Determine the equation of the tangent line to f(x) = 2-x² 1 + x b. Determine the equation of the…

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Q: 3) Find the maximum rate of change of f at the given point P and the direction in which it occurs.…

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Q: 1. Find the slope and the rate of change of the slope with respect to x when t = 90°. x = 2…

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Q: 2. Find (a) the gradient of f at P and (b) the rate of change of the function value in the direction…

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Q: A particle moves along a straight line with velocity function  v(t) = sin t - cos t and its initial…

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Q: 18. Find the directional derivative of * f(x, y) = -2e* cos y at (0, 7) in the direction of v = (-6,…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: Given,

Q: Differentiate the function g(p,9) in derivative and differential form. 5. Given two measurements p+…

A: Given that: Two measurements:   p±∆p and q±∆q

Q: 3. Find the derivative of the function f(x, y, z) = ln (r² + y³ + 4z +5) in the direction of the…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: The maximum value of a function f occurs in the direction of the gradient of the function f and this…

Q: 11. Find the directional derivative of f at the given point in the direction indicated by the angle…

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Q: 2) Find the maximum rate of change of f at the given point P and the direction in which it occurs.…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: Find the derivative of the function at Po in the direction of A. 1(x.y.z) = - 2 e* cos (yz),…

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Q: 2. Let f(r,y) = n: Find the maximum rate of change of f(r, y) at the point (4, 1) and the direction…

A: Given the given function is fx,y=xx-y and the point is 4,1. Apply formula for the maximum rate of…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: Given that: fx,y=2sinxy,               0  ,  5

Q: Find the derivative of the function at Po in the direction of u. X- y g(x,y) = Po(- 1,1), u= 12i +…

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Q: Given y(x) = cos(2x² – 2x), calculate the value of x when y is a maximum and when y is a minimum…

A: Given y(x) = cos(2x2-2x)  first we find the critical points using equation y'(x) = 0 . At critical…

Q: True or False The velocity of a particle whose position at time t is s(t) is the derivative s′(t).

A: Our Aim is to tell whether the statement the velocity of a particle whoseposition at time t is s(t)…

Q: b) Find the gradient of the tangent to the curve y= at the point with x=1.

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Q: Q1: a) Find the directional derivative of S = In(2x +3y) at point (-1,1) in the direction of 4i – 3j…

A: (a) Given S=ln(2x+3y) Differentiate S partially with respect to x and y Sx=22x+3y…

Q: Find the derivative of the function at Po in the direction of u. X-y g(x,y) = Po(- 1,1), u= 12i + 5j…

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Q: 4. Find (a) the gradient of f at P and (b) the rate of change of the function value in the direction…

A: This question is based on gradient of function.

Q: (a) Find the gradient of the curve at the point Q. (b) Given that the product of gradients of…

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Q: Sketch the curve. And indicate the direction of increasing T at T =0

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Q: H.W: Use the chain rule to find the derivative of w= x² + y² with respect to t dw dt with x = cost +…

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Q: 7. Given (x, y)= x' + y² a) Find the derivative at P(1,1) in the direction of " = u,i +u ;j b) In…

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Q: a) Find the derivative of f(x,y) = xe* +cos(xy) at the point (2,0) in the direction of V = 3i – 4 j.

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Q: 3c The gradient of the curve which passes through the point (2,12) is given by 5x + 7 dy dx Find the…

A: The solution is given as

Q: 3. Use the Fundamental Theorem of Calculus Part I to find the derivative of a) [(cost +r +e' )dt b)…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the rate of change of f with respect to t along the curve. f (x.y,z) =y² - sin(x +z),7(1) =…

A: According to the problem, we have

Q: b) Find the value of the derivative of f(x, y, z) = xy + yz + xz with respect to t on the curve x =…

A: There are two methods to do this: One is direct method which we used and other is by chain rule.

Q: Determine the equation of the curve whose tangent line at any point (x, y) is e^- sin x and passes…

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Q: Find the derivative of y = x°e*. O a. y' = 3e*x2(e*+x) O b. y 3x2(e* +1) O c. y = e*x2(x+ 3) O d. y'…

A:

Q: 2. Find (a) the gradient of f at P and (b) the rate of change of the function value in the direction…

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Q: 10. Use differentiation to find the gradient of the curve y = ax sin(bx) at x = 3. 7. -17 b= 19

A: Please refer to the image below

Q: 4) Find the total derivative of the function: a.f(x, y) = ex²+y² 1 c. T(l,g) = 2₁ 2TT. b. z = x siny…

A: Total derivative of a function f(x,y) is given by df=fx dx+fy dywhere fx=∂f∂xfy=∂f∂y

Q: 1. Find the value of the directional derivative at the particular point Po for the given function in…

A: Given that gx,y=y2tan2x ; U→=-32 i^+12 j^ ; P0π3,2We need to find the value of the dorectional…

Q: Determine the gradient and equation of the tangent to the curve f(x, y) = 0 in the point or (a)…

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Q: The parametric equations of a curve are given by x = In (Vi +1) and y = cosh (2t). dy Find the…

A: Use chain rule of differentiation to solve this problem.

Q: Calculate the derivative of the function r(t) i+ cos' (61)j + lIn (2t³)k. t - 2

A: Given : r(t)=-5t-2 i +cos-1(6t)  j +ln2t5 k We have to calculate the derivative of the given…

Q: 5. Let f(x, y) = xe" + cos(xy) and P: (2,0). %3D A. Find the directional derivative of f at P in the…

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Q: 1. Find the gradient of the function f(x, y) = x² sin y. 2. Find the rate of change of the function…

A: The given function is;  f(x,y)=x2 Siny.

Q: Q1: a) Find the directional derivative of S = In(2r +3y) at point (-1,1) in the direction of 4i -3i…

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Q: 1. Find the gradient of the function f(x, y) = x² sin y.

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Q: Given the curve y2º = x in the xy-plane, for what value of y, if any, does the derivative of y with…

A: Differentiation w.r.t to x

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: 4. Find (a) the gradient of f at P and (b) the rate of change of the function value in the direction…

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Q: dy If y = 4x sin (5x), find a. dx b. Let f(x) = In [sin3x], find f'() %3D Find the tangential…

A: We have to find the derivative for the following...