Given x=sin5t and y=cos⁡5t, find the following derivatives as functions of t . a) dy/dx b) d^2y/dx^2

Q: cos ( bVx3 f(x) = a ln sin(cx²)

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Q: 6. Use implicit differentiation to find the following derivatives for the equation tan y = 4 +x?y +…

A: see below the calculation and answer

Q: Find the second derivative (dy/dx) of sin(x) + sin(y) = 1

A:

Q: . 4x?y7 - x° +4y³ + 4) -2x=: 1. e* – sin(y) =x

A: During implicit differentiation, Differentiate both sides with respect to x and then seperate dy/dx…

Q: Find the derivatives of the functions

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Q: Assume that y = sin'x is a differentiable function of x. By differentiating the equation x= sin y…

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Q: Use implicit differentiation  to find dy/dx using the following equation. x5 + sin y = x3y6

A: Given:

Q: Let y be defined implicitly by the equation 2x° + 5y- 4x – 7y = -2. dy at the point (1,0). dx Use…

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Q: Calculate the derivative of: '(14z) cos f(1) = sin (14x) r(e) =O

A: Given query is to find the the derivative of f(x).

Q: The derivative of the function y = sin-1(e* – In x), where Je – In x| < 1, is:

A: Recall ddx(sin-1(x))=11-x2 ddx(ex)=ex ddx(ln(x))=1x

Q: Calculate the derivative of the following function. y= cos (sin (9x))- dy dx

A: We know d(xn)/dx = n.xn-1 d(cos x)/dx = -sin x d(sin x)/dx = cos x d(kx)/dx = k

Q: Find the derivative of the following function. (3x² – 5) y = Cos z + (x² + 1)0* sin 5x

A: Given  y = 3x2-55sin5x + x2+1cosx

Q: Find the derivatives of the functions r = sin√2θ

A: According to the question, we have to find the derivative of the expression, r=sin2θ. The derivative…

Q: Solve for the derivative Arc sin + Arc cos =0 y y

A:

Q: Assume that y = sin-1x is a differentiable function of x. By differentiating the equation x = sin y…

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Q: what is the derivative of arctan(u/1+4u)

A: To determine the first order derivative of the provided function.

Q: Calculate the derivative of the following function. y= cos (6 sin x) dy %3D dx

A: Given that        The function is y= cos(6 sin x) Here we have to find dy/dx .

Q: Find by implicit differentiation. 2+ 4.x = sin(ry²) dy Answer: dx

A: the given implicit function is: 2+4x=sinxy2

Q: Assume that y = sin-1 x is a differentiable function of x. By differentiating the equation x = sin y…

A: The given equation is

Q: Which is the derivative (dy/dx) of y=sin-1 tanx?

A: Formula used   (fog)'(x) = f'(g(x))*g'(x)

Q: Find the second derivative, for y = tan () dy2

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Q: )Find dy using implicit differentiation for sin (y)+ 6ex = y2 with respect to dx

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Q: find the second derivative and simplify the final result 7. y= Arccos(e^2x)

A: To find     d2arccos(e2x)dx2

Q: sin 0 cos 0 1+ 2 In e y = In

A: Consider the function:y=lnsin θ cos θ1+2 ln θ   =lnsin 2θ21+2 ln θ…

Q: Use implicit differentiation to find dy/dx given the equation x-4xy+y =4.

A: implicit differentiation     dfdx = dfdy×dydx in this question we find dydx   and the given equation…

Q: What is the derivative of 0.50 sin 2t+0.30 cos t

A:

Q: Find the derivative of the following function. y = 7x sin -1x dx 히종

A: The given function is,

Q: Can you help me step by step with this problem?

A: Obtain the derivative of the given function as follows.

Q: Use the method of implicit differentiation to solve the equation for dy/dx: x^3y^2+1 = 2xy  and…

A: We differentiate both sides using the product rule and chain rule

Q: Find the second derivative of the function. f(x) = sin(2x?) %3D f "(x) = 16x sin 2x) + 4 cos 22)

A: Given f(x)=sin(2x2) Formula: Derivative of sinx  = cosx Derivative of cosx = -sinx

Q: Find the indicated derivatives: 1. of y = sin(3x + 4y) dx

A: The given function is: y=sin(3x+4y) The derivative of the sine function is: ddxsin(x)=cos(x) From…

Q: Find dy/dx by implicit differentiation for tan-(r²y) = sin(²) + 3xy

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Q: Find the derivative of the function r? In 4y y sin4

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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: Use the quotient rule and the derivatives of the sine and cosine functions to prove that d/dx (cot…

A: we have to find the derivative of the given  expression by using quotient rule

Q: Find the derivatives of the functions r = sin (θ2) cos (2θ)

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Q: Find the derivative. ( cos ft dt x10 COS^/

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Q: Find the requested higher-order derivative for the given function. d?y of y = 3 sin(x) + x² cos(x)…

A: Using Derivatives.

Q: b) Use implicit differentiation to find for the equation yz? -e** cos (4zx)–3y² =4. F. DO NOT use…

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Q: Find the derivative(dy/dx) of following function f(x) = Sin(2x) (x+1)? %3D

A: It is derivative problem.

Q: Find the derivative of the function x3 y = / 9vi sin(?) dt. %3D

A:

Q: what is the derivative to y=sin 2t - 2 cos 2t

A: The given function is y = sin2t – 2cos2t.Find the derivative of the function as follows.

Q: Calculate the derivative of the following functions. y = sin (4x3 + 3x + 1)

A: Consider the given: Find the derivative: y=sin4x3+3x+1Find the derivative w.r.t.…

Q: We know that x =r cos 0 and y =r sin 0, then find the derivative af /ər if 1 f = x2 + y2

A: Given f = 1x2+y2  and x = r cosθy = r sinθ Thus f = 1r cosθ2+r sinθ2= 1r2 cos2θ+r2 sin2θ=…

Q: By computing the first few derivatives and looking for a pattern, find g978 (sin x). dx 978 d978…

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Q: Please show all work

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Q: Find the derivative of the following function. y = 5x sin -1x dy dx

A: We can find dy/dx using product formula as below

Q: 1. sin?(ešin*t) + cos¯'(2t³ – 5)

A: Solution: ddxsin2(esin2t)+cos-1(2t3-5)

Q: Calculate each implicit derivative as indicated. dw/dz and dz/dw 7z^(2)*sin(9w)=9z^(3)*w^(4)

A: Here we will be using product rule as well as chain rule to differentiate the function and we will…