3. Let 2 (-1, 1) and 3+x³, if x < 0, sin x 1, if x ≥ 0. Find the weak u'(x) and u"(x). Justify your answer by the definition of the weak derivatives. u(x) {

Q: 2 a) For the function f(x) = X-3 , find f'(1) by using the definition of derivative.

A:

Q: 2. Let f be defined by { x 0. f(x):= I 0 Using the definition of the derivative, verify if f has a…

A: We need to find derivative.

Q: Let z = a + ib and f(x) = exp (zæ), then find the 1st and 2nd derivative of f(x).

A: Given: f(x)=ezxwhere,z=a+ib

Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: 3. Find the derivative of y with respect to x in the followin u? a) у3 u = 3x' - 2 and u' + 1 b)…

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Q: Compute the following derivatives. Show all your work and indicate which differentiation rule(s) you…

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Q: what is a and b please?

A: Use chain rule to find the h ' (x) and g ' (x).

Q: B3. (a) Let y be a function of x, defined implicitly by the equation x?y + y3 + x = 0. Find the…

A:

Q: 2. Find the anti-derivative of a. f(x) = 2x¹ - 5√√x³7−2e* ++ 3 1 1+x²

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

Q: 2) a) Let f(x) = 2* + 3x7. Find f'(x) and f" (x). b) Find the derivative f'(x) in the following…

A: a.)   Given f(x) = 2x + 3x-1/2 f'(x) , f''(x) are to be calculated. Formulas used here  ** y = ax…

Q: H(w)= (6-5w)* 2. %3D

A: Find your answer below

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: Q. / Find the derivative of y = (In(x²))'n(x²).

A:

Q: 2. If g(x) = (ƒ 03ƒ •4f)(x) = ƒ (3ƒ (4ƒ(x)). Determine gʻ(3), given f(3) = 1, ƒ(4)=1, ƒ'(3) = 2 and…

A:

Q: 6. Use the quotient rule to find the derivative x - Vx y x + Vx (а) 8x2+ 2x y = x - 1 (b) 4х — 1 (c)…

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Q: Find y\\ for each of the following functions: 1- f(x)=sin(xe). 2- f(y) = sin (3y)+ e-2y + In (7y)

A: d(u v) = u dv +v du

Q: Calculate the derivative of the function y(x) given by the equation x2+2xy+2y2=1 under condition…

A: For y=1 we find x

Q: 5. If f(x) = x², g(x) = and h(x) = √x² + 2x, determine the derivative of each composite function. a.…

A: Given: f(x)=x2,g(x)=1x′ and h(x)=x2+2x First find the composite functions and then differentiate

Q: Find the derivative of h(x) = e³ + Vx + lnx. I

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Q: 2. Let f(x) = cos(x). We will take derivatives of this function over and over. (a) Evaluate the…

A: Using standard formula of derivatives.

Q: the derivative for:

A:

Q: 1- If x? + 2xy = y², then 2 is: dx (e) x+1 (a) y-x x+y (c) (d) —х (b) 2x + 2y ソーズ

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Q: Assume that f(x) is differentiable. Find an expression for the derivative of y at x = 3, assuming…

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Q: Let g(x) = xe2r +1. Find g'(x). Don't simplify your answer. (а) 3. Let h(t) sec(t2). Find h"(t).…

A: (a)Given: