(H.W) Find the derivative of the function at Po in the direction of A. 2- h(x, y) = tan-'(G + v3 sin-(), Po (1,1), A = 3i – 2j

Q: Find the derivative of the function f(x) = = sin(x) - 1 cos(2x) + 1 4

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Q: Q2/ A/ Show that the functions f(x) = sin-1() and g(x) = 2tan-Vx, have the same derivative. %3D

A: Given : f(x)= sin-1 ( x-1 / x+1 ) g(x) = 2 tan-1 (√x)

Q: Find derivative of the following functions 1. y= sin^-1 2x^2 2. y= tan^-1 2x^2/5

A: Given 1. y=sin-1(2x2)2. y=tan-1(2x25)

Q: When f(0)=0 and f(pi)=0, what is the derivative of the function  7e^x + 6sin(x), and what is the…

A: Let the given function be:Applying the derivative with respect to x:Derivative of ex is ex and the…

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: 9 tan t Find the derivative of the function y = 2 + 2 sect dy dt

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

Q: 6. Find the tangent line to the function f(x) = 2x cos"(x) (0, 1).

A: To find the slope we need…

Q: Find the value of the derivative (if it exists) at each indicated extremum.           f(x) = cos x/2

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Q: 1. Find the first derivative of the given function given. a. y = sint cos t b. y = 6 tan(2n + 3x)

A: In this question we have to find the first derivate of the given function.

Q: 5. Consider the function f(r, y) = sin(x² + y²). (a) direction of (4,3). Find the derivative of f(r,…

A: The directional derivative is the rate at which the function changes at a point in the direction .…

Q: A-The derivative is y = ln sin 0 cos 0 1+2ln 0

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Q: 7. Compute the derivative of y = tan-(Kr) 1. at the point r = K

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Q: find the derivative of y with respect to the appropriatevariable. y = √(s2 - 1) - sec-1 s

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Q: Find the derivative of y with respect to x. 1 y = cot 16x² - 1 + sec - 1 2 - 1 4x, 4

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Q: COS 2. %3COS

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Q: dy of the function dæ Find the derivative x* In 3y = y sin 3x + et.

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Q: Find the derivative of the function at Po in the direction of A. 1- f(x, y) = 2xy - 3y² , Po ( 5,5),…

A: As per our guideline we are supposed to answer only one question you can repost other in next…

Q: (b) Find a general expression for dy - (x), the (implicit) derivative of y with respect to x, as a…

A: given rθ=2+2cos2θ   for θ∈[0,2π) (b) find a general expression for dydx let  x=rcosθy=rsinθ…

Q: Consider the derivative function h (x) = -sec? (x) + 9. What is the general antiderivative of h?

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Q: Find the derivative of y with respect to x. -1 2х + 3 26) y = sec" 27) y = -sin-1 (5x2 + 2) 28) y =…

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Q: 1. Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: Part 1 : Slope of tangent at (π2, π4) is given by dydx(π2, π4) ⇒y·sin 8x=x·cos 2x⇒ddx(y·sin…

Q: Y=67€ tanhlt

A: To differentiate the expression, y=6t tanht use the product rule, ddxf(x)g(x)=f'(x)g(x)+f(x)g'(x).…

Q: # 5) Find the extrema points for the function f (x) = using the second derivative tes 1+x x2 %3D Fon…

A: To find the extreme points.

Q: Find the 25th derivative of g (0) = cos(40 + a) where a is a real valued constant.

A: The given function is: g(θ)=cos(4θ+α)

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 x, t, or θ, as appropriate.

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Q: Find the derivative of y with respect to x, and 0 as appropriate: y = 6(sin (In 6) + cos (In 6) а.)

A: Given equation is: y=θsinlnθ+coslnθ Differentiate each term of y with respect to θ:…

Q: The third derivative of y = sin is b) y" =-co а) у -sin 8 c) y" = -8sin d) y" =-8cos

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Q: ) .3 Find the derivative of h(x) = cos (2x – 5 %3D

A: Given,            hx=cos42x3-5To find : The derivative of the given function.

Q: a) Find the derivative of y = 2 sin-1 x. b) What is the value of the derivative at x = 0.

A: given

Q: A-The derivative is y = In sin 0 cos 0 1+2 ln 0

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Q: What is the second derivative of y = 2x -+ sin x with respect to x? a. 2 -+ cos x b. 2 ++ cos x -+…

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Q: Find the derivative of the function at Po in the direction of A. g(x, y) = x - (y/x) + V3 sec-…

A: Given problem:-

Q: 3. Find the derivative y'(x) implicitly. cos?x + cos²y = cos (2x + 2y)

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

A: we have to find directional derivative.

Q: Let y be defined implicitly by the following equation as a function of x and z : eyz +sin(tyz) – xyz…

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Q: 2 a) FIND BY IMPLICIT DIFFERENTIATION: x*y³ = -8 %3D dx b) EVALUATE THE DERIVATIVE FROM PART a AT…

A: Given: x4y3=-8

Q: Find the derivative of y with respect to x. 10) y = sin-1 (e6t)

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Q: find the derivative of the function at P0 in the direction of u. h(x, y) = tan-1 (y/x) + sqrt(3)…

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Q: ind the derivative of y with respect to x. y =-cos-16x + 7° 6 6. 1 + (6x + 7)2 81 - (6x + 7)2 O 4.…

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Q: 3. Find the derivative of (a) f(x) = (x + 2 sin x) (1 – 6 cos x), and (b) g(x) = sin x/ 7x

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Q: Q2) Find the derivative of the function at Po in the directi g(x, y) = x – (y²/x) + V3 sec-' (2xy),…

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Q: Determine the derivative of y=tan(cos-'(4x)) -1 A y'= 4x2/1- 16x2 - 4x B y'= V1- 16x2 c) None of the…

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Q: Find the derivative of y= cos with respect to x. -1 The derivative of y= cos with respect to x is 1

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Q: Find the derivative: 1+e5 f(x) = = COS 1.

A: The given function is f(x)=cos1+e5x1-e8x

Q: Ise implicit differentiation to find the specified derivative at the given point. ind dy at the…

A: Given query is to find the derivative of the expression.

Q: 3. Find the derivative of (a) f(x) = (x+ 4 sin æ) (1 – 6 cos a), an (b) sin r g(x) %3D 6x

A: a). Given function is fx=x+4sinx1-6cosx. To find the derivative of given function. Solution: Product…

Q: V=ln( cosn 92) %3D

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Q: 11 with respect to x is The derivative of y = cos - 1

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Q: QS:-Find the first order derivative of each of the following functions: a) y = etan"x + In (sin-x)…

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