Q4) Find the derivatives of the following functions (answer two only): secx a) y = f,c* (t -) dt %3D 2

Q: Find the derivative dydx for the function x=1t+t, y=1t2 at the point t=12.

A: Here given

Q: Compute the indicated derivative using the chain rule. dy x = 1 – t/3, y = 8t – 1; dy %3D

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Q: Find the derivative dy dx dx of the function y = sec (1 + 4 + sin ¹(4 + ²)

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Q: Find the directional derivative of f(x, y) 6x at P(3,0) in the x + Y direction of Q(0,–2). NOTE:…

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Q: Find the first part ial derivatives of f (x, y) = 3y sin(x? +y?).

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Q: Find the directional derivative of f(x, y) 12x at P(4,0) in the x + y direction of Q(1,–1). NOTE:…

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Q: Find the derivative of y = = Ve-5t +1 dy dt ||

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Q: Find the derivative of the function y = 7 tan(4x). dy %3D dx II

A: Given: y=7tan-14x   As we know that; The chain rule; fgx'=f'gx·g'x The Power law: ddxxn=nxn-1 And…

Q: he derivative of f(x,y)=10x^y at (e,1) in the direction of v = is

A: From the expression of the directional derivative:   D.D=∇fpx,y,z·a→a→   Given:…

Q: Find the derivative of the function y = 5 . 5t +3·3. dy dt

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Q: What is the directional derivative of the function f(x.y)-2xy-3y at point p.- (5,5) in the direction…

A: To find: The directional derivative of the function f(x,y)=2xy-3y2 at point P=(5,5) in the direction…

Q: The directional derivative of f(x, y) = 2e* cos y at (0, ) in the direction of v = (-6, 8) is

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Q: By using the definition of the derivative, use a clear diagram to argue that d S(t)dt = f(x). %3D dx…

A: We have to prove that ddx∫axftdt=fx This will be prove by Newton's Leibnitz rule in this rule we…

Q: find the values of the derivatives dy/dx at x=sqrt(3) if y = 1-1/x

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Q: Find the derivative. F(t) = In(sinh(2t)) %3D F'(t) %3D

A: Find the derivative of the function

Q: Find the derivative of the function y = In(3t + 4). %3D dy dt

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

A: We have to find the derivative of the function fx,y=2x2-y2 at the point M=1,1 in the direction…

Q: Find the derivative of the function. -1 y = (3t – 1)(6t – 5) dy dt II

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Q: Calculate the derivative indicated.

A: Since, y=4t-3+3t2  -(i)dydt=ddt4t-3+3t2=-12t-4+6t⇒dydt=-12t-4+6t

Q: Q1. By using the “definition of the derivative" find of y = v2x? %3D dx

A: Explanation and solutions is given below....

Q: Find the derivative of the function at Po in the direction of u. 3x f(x, y) = tan -1 , P0(-2, 3), u…

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Q: Find the derivative of y with respect to z. y=5(2%) dy dz

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Q: Find the derivative. X dt 14) dx lol 0 5t+ 6

A: To find the derivative of given integral.

Q: Calculate the derivative indicated.

A: We have to calculate the indicated derivative drdtt=4 for the given function: r=t-et We know the…

Q: What is the derivative of h(x, y) = e"Y at (2, 3) in the direction at an angle of 7 from the…

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Q: compute the derivatives indicated. F (0, u, v) = sinh(uv+0² ), Fuuð

A: To compute: The derivative Fuuθ. Given information:  The function is Fθ,u,v=sinhuv+θ2. Concept used:…

Q: ) Find the directions in which the directional derivative of f (x,y) =4x2+sin (5 xy) at (1,0) has…

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Q: Determine the derivative of the function defined by h(x, y) = Arctan () + v3Arcsin () %3D at the…

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Q: Find the derivative of y with respect to x. y = sec 1(3x? + 1), x>0 dy dx II

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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…

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Q: By using the "definition of the derivative" find 2 of y = v2x? dx

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Q: With respect to u, what is the derivative of: * 12 בV 2 2 dx Option1 Option3 -'/2 -15

A: Answer is mentioned below -

Q: 4. y2 +2xy 4, find y" Ans. y" = (x+y)

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Q: What is the directional derivative of the function f(x,y) = 2xy- 3y2 at point po= (5,5) in the…

A: Givenf(x,y)=2xy-3y2 ; p0=(5,5) ; u=4i+3jWe need to find directional derivative Duf(5,5)where…

Q: Find the particular anti derivative that satisfies the following conditions: dy/dx=3x+5/sqrt3 of x;…

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Q: The derivative of the function y = sin VE at a = is equal to %3D 4 14

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Q: Find the derivative dy dx || dy dx of the function y = sec (₁ +√4+ sin ¹(4 + ²))

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Q: Find the derivative of y=cos^3w+cos(w^3) dy/dw=

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Q: Find the derivative of y with respect to z. y=3 (2°) dy dz II

A: We have to find the derivative of y with respect to z when y=3z9 Taking log both sides,…

Q: The directional derivative of f(x, y) = e" cos Y at (0, ) in the direction of v = (-6, 8) is

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Q: dw B) Use the chain rule to find the derivative dt of w = x2 + y2 with x cost, y = sint.

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Q: Use the definition of the derivative to compute dy/dx. y=2x^2-3x+1

A: Use the definition of the derivative to compute dy/dx. y=2x^2-3x+1

Q: +Inz 1. Determine the equation of the tangent line to the graph of f(r) = | V3 + 5t5 dt at x = 1.…

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Q: The first derivative of the given function is y = sec?. %3D 2х + 1

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Q: Use the definition of partial derivative of a function f(x, y) = 3x² – xy? to illustrate fi and f2 '

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Q: at dz = (4자) 424-4%.

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Q: The directional derivative of f(x, y) = e" cos y at (0, ) in the direction of v = (-6,8) is

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Q: Find the partial derivative. z = sin (9x'y – 10æy?) dz

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Q: The directional derivative of f(r, y) =-e" cos y at (0, 5) in the direction of v = (-6, 8) is

A: Given that fx,y=-excos y at0,π4and v=-6,8