by s- differentiation find L(te-3t) = 1 .aO (s- 3) 1 .b O (s-3)2 (s+3) .dO (s+3) 2 1.

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: by s-differentiation find L (t cos3t) = %3D s2 (s² +9) s2-3 .b O (s2+3)2 s2 (s²+9)2 s2-9 (s2+9)2

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Q: 7. Suppose that x and y are related by the equation x 2−4y 2=5 and use implicit differentiation…

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Q: Find the third derivative of f(x) = ³/15z + 1. f"" (2) - ab a b √a |a| π sin (a) 2.

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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: Find the derivative of cos(0)d0. du Jo cos(0)de = cos (w²) · 2w • d de So" cos(8)d0 = cos(2w) • d S…

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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 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 differential d8y of the function y=exsinx.

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Q: Find the differential of the function. z = 3t - = zp

A: Differentiate the function: - Differentiation is that the quantitative relation of a small amendment…

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: What is the derivative of (6 x+1)5 (4 x-21)16 (21 x-23)3 (3 x+25)4 y = In with respect to x?…

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Q: Find of the following by implicit differentiation. Show solution. dx y sin x =x2 – 2y • sin x+ sin y…

A: This question is related to derivative.

Q: Find the differential d3y of the function y=xsinhx.

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Q: Q8/ Use implicit differentiation to find of the following curve at the point (2, 3). dx2 2x3 – 3y2 =…

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

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Q: 2. Find y' by implicit differentiation. (5) xy =1+ xy

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Q: b) Find O Using the chain rule to find de x-1 dy of y= dy of y sin 1-xy ) Using the implicit…

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Q: OFind the derivative of the 1 +5 (a). f(z) = %3D T2-5

A: As per the guidelines we can solve only one question at a time so if you need more answers then…

Q: 3. Use the Leibnitz formula for differentiation to find (i) for the function y=sin" xin) (ii) for…

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

Q: 23.3 Use centered difference approximations to estimate the first and second derivatives of y = e*…

A: The formula for the first derivative of a function fx at x=a by centered difference approximation is…

Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

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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: What is the first derivative of the expression (xy)^x = e? Hint: this involves implicit…

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Q: What is the approximate value of the first derivative of S(x)=-0.1x*-0. 15x-0.5x-0.25x-1. 2 at…

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Q: (§5.5, Q34) Calculate the derivative d dæ ), Vi dt.

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Q: 22. Find the derivative of y = arcos(4x) with respect to x. - 4 4 - 4 - 4 В. 1-4x2 С. Vi-(4x) A. D.…

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Q: Evaluate the second derivative of mq4.5.png os (bVx³) f(x) = a ln sin(cx2) if a = 21, b = 0.5, and c…

A: Given that, f(x)=alncosbx3sincx2a=21, b=0.5, c=5Substituting the values of a, b and c, we…

Q: * find the dicredional derivative af the. f omc tion and in the direction of a= [o,3, 37 + find the…

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Q: II. Find by implicit differentiation. dx dy 1. 2x? + 2y? =17 2. x'y - xy = a'b 1_1, 3. x y 4. 2x +…

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Q: Y= In (In2 (1-x))re?

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Q: Calculate differential: f(x) = e-* cos(3x) + 2 of the range [1,2] with h=0.05 Using the backward…

A: Equation is  f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of…

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: Q1) Use implicit differentiation to find dy/dx if a) (3xy + 6)2 = 7y b) x cos(3x + 2y) = y sin x %3D

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Q: (a) Find the first derivative of the function y= la) with respect to x by using the chain rule.

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Q: 29. Prove the following derivatives by using the definition of derivative. (a) (") = n. dx nxn-1

A: topic - derivative and limits

Q: 3. Find the derivative of f(x, y, z) = z2 + ye" at (In 2, 2, 1/2) in the direction in which the…

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Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz,at the point in the direction of A =…

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Q: Find the derivative of y: 1- y = (cos 0)▼2

A: See the details solution in below

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: 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 7 use log differentiation to differentiate to find y prime (dy).   y = sin(x)x

A: Given function y = Sin(x)x , here we need to determine y\'.Let us use logarithmic differentiation.…

Q: 2 e -8; x(0) = 1 dt

A: Solution is given below:

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: (a) Find thẻ đéřivătivė. rivative. 1 y = In(x2 – 6) 3 dy dx (b) Find the derivative. 3 = INVX2 – 6…

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Q: 2) Find second derivative d'F/dt? of 312-2 F? = 13 and find it at (t,F) = (-1,2)

A: We have to find the required second derivative at the given point.

Q: Find the first derivative 1. y = In v4-x2 %3D 2. In(x2 + y2) + 4arctan = 5 y %3D dy x+4 3. Find , if…

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Q: (1) Suppose that y is a function of r satisfying the equation 5x + 10y + 3.ry+ 5y + 6x 0. Use the…

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Q: Compute the derivative of the given function. f (x) 10x-1/4 cos e + 7 sin a %3D -

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Q: Find the differential of the function   y = θ3 sin(6θ)

A: Solution :-