Determine whether the functions f1(x) := x + 1; f2(x) := sin(x); f3(x) := x - 1; f4(x) := 3 are linearly independent.

Q: Find the derivative of the function. A) f(x) = In(x*Vx² - 3)

A: This problem can be solved by using the Chain rule as explained in step 2.

Q: Find the partial derivative. 3 (x² +3x-3y) 2.

A: Given  z = x2+3x-3y4 We have to find ∂z∂x.

Q: Find the derivative of each function. 1. f(x) = 3x* +5x-2 2. g(x)=-4x+5x'-2r+3 3. f(1) = 25+7NP - 4.…

A:

Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: y=57x3+1-3

Q: Find the derivatives of the functions in Exercise

A: Given: y=1+x2x34-x-3 To Find: The derivative of the given function

Q: Find the derivative of y = (4 - 2x³)(2x + x³). O a. y= 12x5+ 16x - 12x² - 8 O b. y = 12x° + 16x³ +…

A: As per our guidelines we are supposed to solve only one question i.e. the first one. For the…

Q: 5. Find the derivative of the function. f(x) = x°/1- 8x x(16-136x) 2/1-Sr x'(16+136x) f (x)3D 2/1-8x…

A: The function is given by,

Q: Find the derivative of  C(x)=(2x3)/(3x4+2)

A:

Q: Prove that for all a, b e R, the function f(x) = 3x - 4x³ + 6x² + ax + b has exactly one point where…

A: f'(x) is increasing  function. But f'(x)  is polynomial of degree 3. So it has exactly one real root…

Q: Determine the derivative of a quadratic function of general form y=ax2+bx+c.

A:

Q: Find the derivatives of the functions in Exercise

A: The derivative of a function is the rate of change of the function with respect to the function…

Q: Find the derivative of fG Cos' (3x²) 2. %3D

A: Consider the given function:…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x) e2t2…

A:

Q: Find the derivatives of the functions in Exercise

A:

Q: Find the derivative of f(x) = (x-2x)2 A) f'(x) = 6x5 - 12x3+ 8x B) f'(x) = 6x5- 16x3 + 8x %3D C)…

A: Here we find the derivatives of function.

Q: Find the second, third, and fourth order derivatives of: y= f(x )= ax7 + bx3 + c y= f(x) = 3x/1-x…

A: It is simple derivative

Q: Find the derivative of the function. y = In (8x 3- x 2) 24x-2 8x2 - x %3D 8x-2 O 8x2 -x 24x-2 8x2…

A:

Q: Find the derivatives of the functions in Exercise

A: The given function is u=5x+12x.

Q: Find the derivatives of the functions in Exercise

A: The given function is y=x-35+π32

Q: Find the derivative of G(x)= (3 – 2x)10 %3D - u = g(x) =| g'(x) = f (u) = ..... f'(u) = G'(x) =…

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Q: =) f(x) = x²e¬4x

A:

Q: Find the derivatives of the functions in Exercise

A: Find the derivatives of the functions in Exercise

Q: In Exercises 11–28, calculate the derivative with respect to x of the other variable appearing in…

A: Given: y4-2y=4x3+x for finding value of dydx, we differentiating given expression with respect to x

Q: Obtain the first and second derivative of the following real-valued functions 1. ƒ : R → R, such…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find the derivatives of the functions in Exercises 27. y = x2sin^2 (2x2)           28. y = x^-2sin^2…

A: To find derivative of 1) y=x2sin2(2x2)2y=x-2sin2(x3)

Q: 3. f(x) = (2x + 1)3 4. f(x) = V7 + V3x + 1

A:

Q: Compute the derivative of 6x2 f(x) = In(r) %3D

A: We have to find derivative

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the func - 2t dt g(x) =…

A:

Q: Find the derivative of the function. x3 y -1 -2x3+3x2 y's (x- 1)2 y'= 2x-3x2 (x-1)2 y'= 2x3+ 332 (x-…

A:

Q: 1. f(x) = V3x +2 2. f(x) = 2х-3. 4 %3D 5x+1

A: We know quotient rule of differentiation as follows  ddx{f(x)g(x)} = g(x) f'(x) - f(x) g'(x){ g(x)}2…

Q: The derivative of is f (x) = 3x* + 7x² + 5x + 2 %3D

A: Given, f(x) = 3x4 +7x2 +5x +2

Q: 2x + 9y = 6x²y – 5x³ 2.

A:

Q: Find the derivative for f (x) = V4 + e2x a. e2x /4+ e2x b. 1 2v2e2x xe2x-1 /4+ e2x C.

A: To find the derivative of fx=4+e2x.

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: Find the differential of the function.

A: Differentials are infinitely small quantities. We usually write differentials dx, dy, dt (and so…

Q: Use the chain rule to find the derivative of f(x) = 2e5a* + 9x³ %3D f' (x) =

A: We have to find

Q: Find the derivative of the function at the given point in the direction of A. 3) f(x, y, z) = -10x+…

A: Here initially we need to find out the partial derivative of the given function to find out the…

Q: Find the linearization of the function at a. 1. f(x) = x^4 + 3x^2, a = -1 2. f(x) = sin x, a =…

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Q: Find the derivative of the function. u(x) = (x2 + 1)9x2 − 1 u'(x) =

A: The function u(x) is:

Q: Find the derivative of the function. y = (3x+1)(x*-6)s O a. y' = 9(3x+1)2(x+-6)°+32x(3x+1}³(x4-6) а.…

A:

Q: Find the derivative of y = x²( - %3D x2+1

A:

Q: Find the derivative of the function. %3D X-1 y'= 23,3,2 (x-12 y = -2+3x2 (x- 12 y = 203ి - మెపి (x -…

A:

Q: Use Part I of the Fundamental Theorem of Calculus to find the derivative of g(x) = 3x 2x и +1 du и -…

A: Giveng(x)=∫3x2xu+1u-2du

Q: Find the derivative of the function. 4x - 5 8x + 1 dx dx d (8x + 1) • (4x - 5)– (4x – 5) • d (8x+1)…

A: Explanation of the answer is as follows

Q: Find the derivative of the function. g(x) = [*- 1 -dt -5 2+4 10 а. 841 b. 2x (x²+ 4)² 1 С. x²+4

A:

Q: • 5x²+1 (t²-t) dx F(x) =

A:

Q: Find the derivative of the function. g (x) = 4x(3x + 2)’ %3D

A: The given function is gx=4x3x+25

Q: Find the derivative of the function. 3x-4 %3D 2. X+6x y' = ]

A:

Q: Find f'(x) (the derivative of f(x)) if f(x) = 7x'3 - 2x'2 + 4x - %3D 5. O 21x^2 - 4x + 4 + C O 21x^2…

A: