2ae2x 2ae2x. Let a be a real valued constant. Find the derivative with respect to x: y = -1 4xe2x O y (x) = (2ae2x – 1)² -8ae2x O y (x) = (2ae2x – 1) O y (x) = -4ae2x (2ae2x – 1)° 2ae2x O y (x) = (2ae2x – 1)

Q: h(x)=In( x² ) +(x³-1 ) es*-10 Calculate the derivative at x=2, that is h'(2)=

A: Use chain rule of differentiation First differentiate with respect to x and then put x =2

Q: Find the derivative of y with respect to x. y = tan (In 3x) O A. 1+(In 3x) 21 O B. x(1 + ( In 3x)) 1…

A: Given: The function y=tan-1ln3x, To determine: The derivative of y with respect to x,

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: 2. Find the derivative of the following functions. (a). g(x) = cos (2x + 1) (b)," f(x) = In (x² – 4)…

A: To find the derivative of the functions

Q: Find the second derivative of the function y=x(x² – 1)² A) None of the given choices B) 2x(5x2 - 6)…

A:

Q: 7. Let f(x + iy) = (3x²y – y³) + i(3xy² – x³). Decide if f (x + iy) is differentiable and if it is,…

A: Given function is  fx+iy=3x2y-y3+i3xy2-x3                       (i) The function f is differentiable…

Q: Determine the derivative of y (x) = ( 3 x² + 11 x + 4 )³ e-6 x with respect to x. y '(x) =

A: topic - derivative of a function

Q: 1. Determine the first derivative of the functions below with the rules for deriving the function:…

A: A Given function is y=4x3+32. Use formula ddxxn=nxn−1 Differentiate  y=4x3+32 by using the chain…

Q: Find the derivative of the given function. y = In (- 25x² + 3x) y' =D %3D (Турe an exact answer.)

A: Solving by derivative rule

Q: 3. Find the derivative. sh (a)l= - पक) (a) f(x) = x2 cos x +x tan r (b) h(x) = e" (x² + 4x) %3D t2…

A:

Q: Find the derivative of y with respect to x. + 1 5) y = sec-16x + -54 A) – 1 + (6x + 1)2 54 C) (6x +…

A:

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y=x" In x - O A. 4x-x O B. x*…

A: The function is given as y=x4 ln(x)-13x3 Differentiate the above function w.r.t 'x' y'x=ddxx4…

Q: 4- Calculate the second derivative of the function y = f (x) defined by the equation x3 + y3 +3xy +…

A:

Q: Find the derivatives of the functions in Exercise

A:

Q: 1 y = x²-1 Using differential, draw the function

A: This is a problem related to differentiation. Based on the general formula and concept we will…

Q: Given y = (ax? + bx )e -bx where a and b are constants. Find derivative of y with respect to x. e-bx…

A:

Q: 1. Find the derivatives of each of these functions: a. y = ln (4x² + 4) b. y = 22² c. y = 25x+7…

A:

Q: 1. Find the derivative (dy/dx) of the following functions: In a) y = 3x7- 7x³ +21x2 In b) y = (x2 +…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the…

Q: (b) Calculate the derivatives of the following functions. (i) y = e5x (ii) y = etan 3x (iii) y =…

A: derivative

Q: 20. Find the derivative of the function. y = 9cos(2x) a. y'=-18sin(2x) b. y' =18sin(2x) c.…

A: Option (a) is the correct option. Differentiate y using the chain rule.…

Q: 2 3 1. Determine the derivative to y² = x³ + y² + 2xy

A: Given problem:- Determine the derivative to y2 = x3 + y3 + 2xy

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

A:

Q: 3. Find the derivative of y with respect to x in the following functions : 18x'y (ans.: (3x-2) a)…

A:

Q: 4- Calculate the second derivative of the function y = f(x) defined by the equation x³ + y3 +3xy +…

A: The given function is: x3+y3+3xy+3y2+6x+6y=0

Q: Find the derivative of the function. y = (x + 1)²(x² + 1) ~ 3 ...... - 2(x + 1)(2x² – 3x – 1) OA.…

A: Given:- y = (x+1)2(x2+1)-3 To find :- Derivative ol y

Q: Which of the following shows how to find the derivative of f(x)? 3e* f(x) |3D ex-7 (ae(*-7) -…

A:

Q: 1. Find the derivative of each given function with respect to x. (i) F(x) = | t dt 1+ t2' (ii) G(x)…

A: FUNDAMENTAL THEOREM CALCULUS If f(x) is continuous over the interval [a,b] and the function F(x) is…

Q: 9. Find the derivative of y = xe3-x (A)e3-x? (B) 0 (C) e³-x*(1– 2x?) (D)–2xe³-x² (E) e3-x*(1+ 2x²)

A: Given : y = xe3-x2

Q: What is the derivative of y = (x2 + 1) e-3 ? O y = (x² +1) (e-3) + xe² - 3 O y = (x² +1) (e*-3) +…

A: It is required to find the derivative of the given function.

Q: 3. Find the derivative of ywith respect to x in the following functions: 18x y (3x-2 + 4x) x'- 3 a)…

A: Please see the explanation below

Q: We want to find functions u₁(x) and u₂(x) such that yp = U₁Y₁+U₂Y₂ is a particular solution. We can…

A:

Q: 11. Find the derivative of the following function. y=2-6e a y'=54r°e b. y' = -54x°e- c. y' = 6e d.…

A: Given function is

Q: Find the derivative of the function. y = (3x + 1)°(x+ - 6)° A y=(32x +9)(3x +1) (x*-6)° B y' = 9(3x…

A:

Q: h(x) = In (2x-2)+(x² +1)e³x-6 %D Calculate the derivative at x=2, that is h'(2)=

A: calculate the derivative as shown below: h'x=ddxln2x-2+x2+1e3x-6…

Q: Find the first derivative of y with respect to x (y') of the given function. y = ((U^2 - 1) / (U^2…

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: Find the derivative of y= (x³-1) /(x-1). O a. 2x -1 O b. 2x -3 O c. 2x + 3 O d. 2x + 1

A:

Q: The derivative of the function y = In (* + 1) (* - 1) is O y = O y = :- - 1 e+1 + -2 +1 ||

A: Question is solved.

Q: Find the derivatives of the functions y = (1 + 2x)e-2x

A:

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 17) y =x*in x -x3 A) 4x3 - x2…

A: Given, Find derivative of y=x4lnx-13x3 with respect to x

Q: C. Apply the chain rule to find the derivative 1. y = (8 - 3x )3 3. y = (1-x)7 2. y = V2x + 1

A:

Q: Find dy for the given values of x and Ax. 3 y =x° - 6x +8; x = 1; Ax = - 0.1 - 6x + 8; x = 1; Ax = -…

A:

Q: Find the derivative of the function. - c() (수 1 - e9x 1 + e9x y = cos y' = 18e9z sin + e&= )…

A:

Q: 25. Find the derivative of the function. y = (1+ 3x)e - 3x O A. - 9e - 3x 3x В. - 3(1 + 3х)е - 3x -…

A:

Q: x°y- xy? +x² + y² = 0 %3D

A: Use d(UV) = VdU+ UdV

Q: 9. The derivative of the graph x+y² D5 with respect to time is c-2y+ 20 C. a. y +x d. -y 2x +2y

A: Q 9 Given that: The graph: x2+y2=25

Q: Q/2: Find the derivative of the following: (a) y = (x²ln x)* (b) y = In 1-x

A: According to power rule of differentiation . According to product rule of differentiation .

Q: Get the first order derivative of the function x? – 3x5y* + 2x = 5. y 2xy-15x*y*+6x² 5-x²+15x=y* a.…

A:

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