1. Find the derivatives of the given functions. a. y= arccos(x b. y = In (arctan x) c. y= csc (2u+1) d. f(x) = tan (e**)

Q: b) Find the derivatives of the following functions: (i) 3x+4 y = tan x+5 (ii) y = e* -cos3x + x log.…

A: Derivatives

Q: The graph of x3 + y3 = 9xy is the folium of Descartes. Find dy/dx by implicit differentiation.

A: x3+y3=9xy

Q: Find the 90th derivative of y = cos 2x. %D

A: dy/dx of cos2x=-2sin2x.

Q: Is it possible to evaluate the anti-derivative below? | (x + 1) cOS (2x) cos (x2) dx

A:

Q: 1. Find the derivative of the following using implicit differentiation. TYON b. BARZ c. y = sec(x +…

A: Since we only answer up to 3 subparts, we'll answer the first 3. Please resubmit the question and…

Q: 4.62. Evaluate the derivative of the Gamma function and see dT'(x) r'(x) = dx ' (In t)e"'dt

A: To differentiate the gamma function:         Γ(x) = ∫0∞tx-1e-tdt Integral definition of gamma…

Q: (4) 3. Use implicit differentiation to find dy/dx of the following: x² - 5xy + y³ = 21

A: As per policy only first question is answered. Please refer to the image below

Q: 1) Find the derivative of y = e" tan x

A: As we know that; The chain rule; fgx'=f'gx·g'x And ddxex=exddxtanx=sec2x Given: y=etanx

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

A:

Q: 4. Determine the following derivatives without simplifying either before or after. d a. dx -…

A: As per the guidelines I am supposed to do the first three parts of a multipart question.  So I am…

Q: Find the slope of the curve 2xy = In(e*) sin(x) at the point (2,2)

A: to find the slope differentiate  the equation with respect to x .

Q: Find the derivatives of the functions in Exercise . y = (1 + x2) e^tan-1 x

A: Given,          y=(1+x2) etan-1x

Q: Compute the derivative d/dx of the following functions: y = 2 sec x − csc x x cos^2(4x)…

A: y = 2 sec x − csc xDifferentiate w.r.t.xdydx=ddx( 2 sec x − csc…

Q: Find the differential equaiton corresponding th y= a cos(log x) +b sin(log x) where a and b are…

A: Differential equation formation

Q: 5. As a particle moves through the first quadrant, its a and y coordinates are functions of time t,…

A: Given tan(theta)=y/x

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

A: Given that

Q: (1) (a) Find the derivatives of functions f(x) = e2 and g(x) = 5æ?. (b) Compute the definite…

A:

Q: Let z=sin (y 2- 4x). Find the rate of change of z with respect to y at the point (2, 1) with x held…

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Q: d² (¤Arctan x dx?

A: To find the following derivative of the given function.d2dx2x arctan x

Q: Find derivative /differential of each of the following functions by using the appropriate formula.…

A: y=x2 e2x  dy / dx  =?

Q: 9. Find dy/dx by implicit differentiation of y? = In(x), at (e36,6).

A:

Q: Find the derivative of y with respect to 0. y = In (4 cos20) dy de

A: Given, y = ln4cos2θ  We have to find dydθ

Q: Find the derivatives of the functions in Exercise y = t tan-1 t - 1/2 ln t

A: To find: The derivative of y=t·tan-1t-12ln t Concept used: Product rule of derivative: uv'=u·v'+v·u'…

Q: 4 For the function y = 1 e - dy the second order derivative dx? is

A: Given that a function and find second derivative of this function (d2y/dx2). We know that d(xn)/dx =…

Q: Q-1: find the derivative of y with respect to the given indepe 1. y = In(Inx) 2. y = In(In(Inx)) x…

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Q: Find the derivatives of: d/dx (ex-e-x/ex-e-x) And the derivatives of: f(x)=ln((2x+1)3/(3x-1)4)

A: the given expressions is: dex-e-xex-e-xdx the given function is: f(x)=ln2x+133x-14

Q: find the first & second derivative of fox)=e 2. Cosx.

A: Given: The function fx=x2excosx, To find: First and second derivative of given function fx.

Q: 1. Find the derivative of the following functions (dy/dx) at x=Tt/4 cos x2 1– sin x2 y= 2. Find the…

A: We have to find the derivatives of given function at x=π/4  1. y= cosx2/(1-sinx2) 2. y=x3sin3xcos3x

Q: (a) Find thne derivative. y = In(4x – 6) – 3 In(x) dy dx

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: (4) 3. Use implicit differentiation to find dy/dx of the following: x2 – 6xy + y3 = 24

A:

Q: 4. Find the indicated higher-order derivative of the given functions. d'y а. у %3D 8е* + sin x; dx7…

A:

Q: 1. 2x'y² + 4yx² = 6. Find dy/dx at (1, 1) by i- %3D

A: Here we have, 2x3y2+4yx2=6 ................... (1)  Differentiate with respect to x

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

A: To compute the derivative of the function.

Q: (c) Find dy/dx by implicit differentiation cos(x² y) = x

A: We are given, cos(x2y) = x We need to find dy/dx

Q: 7) Find the derivatives in a) y = (1+e')lnt

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find the derivatives of the given functions. a. y = [ Arc sec(tan x)|· e »<2x

A: use logarithmic function to evaluate the derivative.

Q: 1. Calculate the derivative of the following function. y= V2x + 19 dx 2. Calculate the derivative of…

A:

Q: Use the appropriate form of the chain rule to find the derivatives. 5.x2 + 5y2 + z²; x psin ф сos 0,…

A:

Q: 1. Find the respect y = 2x5-x² 3x - 20 derivatives with to X using dy using o 12-1

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 14. Consider the curve defined by x2y2 - 3x2 - 6y2 0. dy a. Use implicit differentiation to find :…

A:

Q: 1. Given dx [arccot u] = find the first derivative with respect to x of arccot v2x + 2. 1+u?

A:

Q: 2. In each case, find the derivative d. (a) z = x³ – y² and x(t) = cos 2t and y(t) = e-3t, (b) z =…

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Q: Find the third order derivative of y = In(cos(2x)). A. y' = -40sec? (2x)tan(2x) B. y' = -80sec?…

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Q: Find the derivative of y with respect to x: ,2 2 X'e y = log,2 x+2) Evaluate the integral: -1 cos…

A:

Q: 10. Compute the central difference approximations of O(h^4 ) for the first derivative of y =cos(x) +…

A: Solution is below

Q: Let -sin (y-4x) Find the rate of change of z with respect to y at the point (2, 1) with x held…

A:

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

A: Let's find derivative of given  function.

Q: 2. Y= 2 Arccos (1-5+ V4x – x²

A: Let's find.

Q: Find the derivative of y with respect to x. y = sin -1(et) OA. 5e 5t /1- e 10t O B. - 5 e 5t /1- e…

A: We have to find