A function x = x(y) is defined implicitly by the equation cos (x y) = -yš +4 x y+4x Find using implicit differentiation the expression for the derivative x' in terms of x and y.

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: Find the derivative of the function using implicit differentiation. 1.) x²+y²= 16

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the derivative of cos(xy^2) = -3y using implicit differentiation

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Q: Find the derivative of the function.

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Q: Find y’ if y=cos(ln(x^2 +1)) y’(0)= Use implicit differentiation to find the equation of the tangent…

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Q: Find the derivative of 2 cos x 1. f(x) x+1

A: As we know that: The Power rule: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2 Given: fx=2cosxx+1

Q: Find the derivative of the function. f(x) = sin(x) cos(5 – x²) f'(x) =

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Q: 3- Find the derivative of sinx +x /2+cos x.

A: The given function is fx=sinx+x2+cosx. The formula for differentiation for the sum of functions is…

Q: Find the derivative y by implicit differentiation 4xy2=5x+8

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Q: Find the first derivative x2y + y2-2xy =5                   Use implicit differentiation

A: The given equation is x2y+y2-2xy=5. Assume y is a function of x. By implicit differentiation, find…

Q: 2х- 3 3. У3 5x +1

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Q: Find the second derivative of the function 2 f(x) = sin (3x). Show your work.

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Q: Find the derivative of the function. f(x) = ln   x + 2 x − 2

A: Given,            fx=lnx+2x-2

Q: Find the second derivative of the function.

A: Given: fx=x cosx Now to find the derivative of the given function, Differentiate given function with…

Q: find implicit derivative of x^3 + x tan^-1 y = e^y

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Q: Find the derivative of the function 3 tan (x- 2 1 x y

A: Given:

Q: ind the derivative of y=(x-1)(2x-x2)1/2 - arccos(x-1)

A: Given function: y=x-12x-x2-arccosx-1

Q: 14. f(x) = 2 +3cos x

A: using basic properties and application of derivation we will solve this question.

Q: 6. Find the derivative of f(x) = x² – 3x. Use the result to find the slope of the tangent line to…

A: By using differentiation. and definition of tangent at point.

Q: a) Find the derivative of the function using limits: f (x) = 2x+1 b) Find an equation of the tangent…

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Q: Find the derivative of the function .

A: Given a function f(x)=2x3+3 cos x f(x)=2(x)1/3+3 cos x      =2x-1/3+3 cos x We, use the following…

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: Find the derivative of y with respect to x using implicit differentiation in the equation *'y =…

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Q: Find the derivative of the function. 10 f(x) = 3 + 2cos x

A: Recall: dxndx=n xn-1 d(cos ax)dx= a(- sin ax) dc1f(x)±c2 g(x) dx= c1d[f(x)]dx± c2d[g(x)]dx

Q: 3// By using logarithmic differentiation and with respect to independent variable x, find the…

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Q: Find the derivative of y with respect to x Y=5 ln (3 ln x)

A: Given, y=5 ln (3 ln x) We have to find derivative of y with respect to x.

Q: Find the derivative of y with respect to x. y = csc-1(x5 + 1) ; x > 0

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Q: Find the derivative of the function. h(x) = ln[(−6x + 3)(x + 3)]

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Q: 3. Find the derivative of f(x). (a) f(x) = e cos x (b) f(x) = (2x³ 4x-¹) cotx -

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Q: Find the derivative of the function using implicit differentiation.  1.) x²y + y²x = -2  2.) √(xy)…

A: 1.) x²y + y²x = -2    2.) √(xy) = x²y+1 ntiderivatives for integral notation. (x+7) dx

Q: Compute the derivative of the function y = 6 cos- (4x) at the point x = (Use symbolic notation and…

A: Solution ) y = 6 cos-14x Differentiate with respect to x  y' = 6 d/dx (cos-14x) [ we know that  d/dx…

Q: Find the derivatives of inverse function: y = sec-1squareroot of 1 + x2 AND…

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Q: sin x.cos x- 8- Find y' for y = In x 9- Use the definition of differentiation to find the first…

A: Given  y=sin x cos x2ln x and f(x)=3x2 We need to differentiate these functions wrt x. This can be…

Q: Use implicit differentiation to find the derivative in the form dy/dx.

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Q: Find the derivative of f(x) = ln(2x^3 + x).

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Q: Find the derivative of x^2-xy^2=e^y using the implicit differentiation.

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Q: Find the equation of the tangent line to the curve given by f(x) = x2 ln x at the point  (1, 0)

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Q: Find the derivative of the function using implicit differentiation.  1.) x³-3x²y+2xy²=12 2.) x²-y²…

A: This question is related to implicit differentiation, We will solve it using given information.

Q: The function f(x) whose derivative is sin x and whose graph passes through the point(0, 2)​

A: we have to find the function f(x) whose derivative is sinx and whose graph passes through the point…

Q: Find the first derivative of h(x) if h(x) = cos (x – 2x) -

A: h(x) = cos2(x3-2x)

Q: Solve for the derivative of the Trigonometric Differentiation. 1. y = sin (5x) + 3x cos (5x) 2. y…

A: given y=sin5x+3cos5xdiffrentiate w.r.t. xdydx=ddxsin5x+3cos5xdydx=ddx(sin5x)+ddx(3cos5x)we know that…

Q: Example 2.35: Using Implicit Differentiation to Find a Second Derivative d'y dx Find if x +y² = 25.

A: Explanation of the answer is as follows

Q: Show that x + yx−1 = 1 and y = x − x2 define the same curve [except that (0, 0) is not a solution of…

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Q: 3 sin(x) +x² In(x) – 2x Find the derivative of f(x) = using derivative rules.

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Q: Find the derivative of the function. f(x) = (2x2 − x)ln x   f'(x)=

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Q: Given f(x)=x(x-1). a) Find first derivatives of function f(x) using product rule and chain rule.

A: Our objective is to find the derivative and critical points.