3. Find the derivative of the given exponential function w e2t (2 cost + sin t)

Q: 2. Calculate the derivative of the following y= (*- 3 + Sx) B. Ytan (x+ Se-2) (4x + 3) Tx-2) A. C.…

A:

Q: 4. Find the second derivative for the following functions : a) y=(x+!)' (ans.:6x +6+ 12) x' b)…

A: (a)

Q: Find the derivative of the function. 2 a) f(x) = x² ln(x) b) g(x) = 2" + log, (x + 5) +ez c) y =…

A: We have to find the derivative.

Q: Find the function with derivative f′(x)=e^3x that passes through the point P=(0,8/3) f(x)=

A:

Q: 2. Calculate the derivative of the following. B. Y= tan(x+ 5r-2) C. y=- (E +24) :(2-)

A:

Q: 1. Find the derivative of the following: 1² + 2r + 1 a) f(1) = r3 - 5x + 3 b) G(2) - VP+1 dt e) y…

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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: y = (e*+4 +2)/(e2+3x +1)

A: y=e-3x+4+2e2+3x+1

Q: 3. Find the value(s) of k for which y = e satisfies the equation y+2y' = y" derivative) (note: y" is…

A: k = 1+2, 1-2explanation is given in below step

Q: Calculate the second and the third derivative of y =ar y" -(8/(pix^5)) -(48/(nix^7))

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Q: OFind the second derivative of y = 4Vx + E + 10

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Q: 2. Given x³+ y3 = 6xy dy? a. Use Implicit differentiation to find ? dx b. Find the equation of the…

A: a)

Q: Find the derivative of f(x) = In(e +4) 1 O 3e? e+4 3e3

A: We use the chain rule

Q: 1. Find and simplify the indicated derivative: (a) D: [e¯t sin(2t)]

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Q: Evaluate the second derivative of e e22.1.png acos(b/x) f(x) = x2 if a = 123 and b = 0.5 at x = 6…

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Q: 17. a. s = ln(4x) Inz I b. 1 IN C. IN d. 1 4x

A:

Q: Q1: Find the derivative of the functions. 5- y = (csche)(1- In csche) 6- y = log3 (1 + 0 In 3) %3D

A: 5. y=cschθ1-ln cschθ6. y=log31+θ ln3

Q: Find the equation of the line tangent to xe^1−x at x = 1 and x/e * ln x at x=e.

A: To determine the tangent lines to the curve using derivatives

Q: 5. Use the chain rule to find the derivatives of (a) y = log; V4 + 1 (b) y = (x – e-")²

A:

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

A: Given that

Q: Q5:The derivative of: y(Y)= log,(sin (Y )cos (Y ))- log,(2*e

A:

Q: Find the first and second derivatives of the functions w = ez(z - 1)(z2 + 1)

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Q: Find the function with derivative f'(x) = e8 that passes through the point P= (0,7/8).

A: We are given a diierentrial equatrion[f'(x)=e8x ] and a pssing point (0, 7/8) of the same  we need…

Q: 4) a) Determine the derivative dx of the following functions y = 3** b) 1-3- 3e² 1² c) y d) y =…

A: We have to find the derivative.

Q: 2. If y = x +3x-2x+1, find the values of the following e. derivative, i. У"(2) d'y ii. dx ii. y" (2)

A: Please refer to the image below

Q: Use the theorem of Leibniz in the following problems: 1. Obtain the n'th derivative of: x2y [x?y") +…

A: The objective of the question is determine the nth derivative of the given equation.

Q: 1. Applying the definition of derivative, a. find dy/dx in each of the following: 1 a. 1] y = - x² –…

A:

Q: /4 Find the derivative of y with respect to t. (a) y = In(3te-1) (b) y = esin t (In t² + 1) (c) y =…

A: Given functions,  (a)  y=ln3te-1 (b)  y=esintlnt2+1 (c)  y=tlog3e(sint)(ln3) The objective is to…

Q: 3 (a) Find the derivative of the function y = (t3 + 1)10 dt

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Q: Find an equation of the tangent line to the gra 26. 1+ln(xy) e (1, 1)

A: Obtain the derivative of the function with respect to x as follows.

Q: 1. Find the anti-derivative of the following. e" (x + 1) dx x2

A: From the given information. Anti-derivative has to be calculated to the following expression.

Q: 2. Find the derivative of each function. # 45 : y = In(1+e2") b. # 47: y = a. et +e-a

A: Chain rule: If F(x) is a composite function f(g(x)) and if F(x) is differentiable, then the…

Q: Find the differential of the given function y = xcosx

A: To differentiate

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

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Q: Find the derivative of the function f(x) = Jet – In(/x) (e+12 – 1) O (e:/2 – 1/x)

A:

Q: Calculate the derivative of the following function. y=6 log 3 (x - 9) d 6 log 3 (x - 9) =D dx

A: d/dx [ f(x) ] = 1/ f(x) * d/dx[f(x)]

Q: Find the slope of the tangent line to the exponential function at the point (0, 1). y 2 1 (0, 1) -2…

A:

Q: 10. Solve for the derivative of y IMPLICITLY 22 + Væ³ + 2y= y²

A: Note: According to our expert guidelines only first individual question is to be answered, kindly…

Q: Find the derivative of the following exponential functions: ans. y' = -4e-4x 1. y = e-4x ans. y' =…

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Q: Find the derivative of the function. r(x) = In| 4x + e* | Oa. 4+4e4* 4x +e*x O b. none of these…

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Q: IV. Obtain the 2nd Derivative of the given function. 7. 4y – xy? 1

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Q: Solve for the derivative of the following Exponential Differentiation. 1. y = 92x^2 + 3x +1 2. y =…

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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) Find the derivative of the following: In xy = e*+y 4. %3D y = esint (In t² + 1) 5. y = In e 1+e…

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Q: 2. Find the derivatives of the following functions. a) y = (log2 x)3¬*

A: Given information: The function is y=log2x3-x. Calculation: Find the derivative of the function. Use…

Q: 11. 5 4 Determine the derivative of y=x° – x* + 6. - Enter your next step here dy ab a + JT 00 () dx…

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Q: Find the first derivative of exte-2 y = = ܘ ܘ e+ܫܐܕ 2k+e ye+e 2 ܪܢܐ e+e 2 ܢܐܨ ܐ e+e

A: