Suppose the nonzero function f(x) is infinitely differentiable and that f'(x) = -3f(x) for all a with f(0) = 1. Find the first, second, third and n-th derivative of f at x = 0. As well, find the of f

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y= ln x3

A: Given:

Q: Find the derivative, dy/dx: y = x² In x3 ý =- 2 1-4 ln x x³ In? x 3. ý = -2 In x – 2x | y = --(- 3…

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Q: Find the derivative of the function by the limit process. f(x)= 2/x2

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Q: Find the second derivative for the functions defined as follows g(x) = 4x(ln x)

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Q: Find the derivative of arctan(x² + 1) -2x O f' (x) = -2a2 – a4 2x f' (æ) = x² +2 2x f' (x) x4+2x²+2…

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Q: 4. Calculate the derivative of the given function directly from the definition of derivative y = v2x…

A: Given function is  y=√(2x+1)

Q: Find the derivative of the function by the limit process.

A: Given: fx=x2+x-3 To Find: The derivative of the given function by the limit process

Q: Compute the derivative of f(x) = 7 ln (x + 10) + In (x³ ): Answer: f'(x) =

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Q: find the derivative of f (x) at the designated value of x. f (x) = 1x at x = 1/16

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Q: Find the derivative of f(x) = 1 at x = 3

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Q: find the derivative of y with respect to the appropriatevariable. y = x sin-1 x + √(1 - x2)

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Q: Show that r sin (1/x) fails to have a derivative at r = 0 and even the one-sided limits (lim,-0+ (f…

A: We will prove the given statement.

Q: 1 Find the first derivative given that f(x) = xdx +

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Q: 2. Find the first derivative given that f(x)=x√√x + 1 x²√x

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Q: find the derivative of f (x) at the designated value of x. f (x) = x3 at x = 12

A: The derivative of a function can be calculated by differentiating both sides of the function with…

Q: Find the derivative of the function.

A: Given that, f(x)=ln(x-1)   As we know, ddxln(x)=1x Chain Rule Of derivative, If…

Q: find the derivative of y with respect to the appropriatevariable. y = cos-1 (x2)

A: Given function is y=cos-1x2. Chain rule of differentiation states that: ddxfgx=f'gx·g'x…

Q: Give an example of a function f (x) that has one positive derivative on (−1,0) and a negative…

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Q: 4. Find the first order derivative with respe. to x of the function u = In/x2 + y2 + z2 %3!

A: The function is u=lnx2+y2+z2

Q: Find the derivative of the function f(x) = 5ª+x² + log3 (In x). %3D

A: To find the derivative of the given function.

Q: Find the derivative of y with respect to x.

A: Assume z=x^5+1. Then found derivative dy/dx using the chain rule.

Q: find the derivative for  h(x) = 3e ^ -x * ln(2x+1)

A: Using product rule of derivative In order to solve the given problem.

Q: 3/x +1 f(x) = X+2 at x = -1

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Q: 3x g(x)=e* In(4x+1) (с)

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Q: 2. Determine the second derivative of f(x) = x²e²* at x = -2 with a step-size of h=0.50 using…

A: Given function f(x)=x2e2x. The objective is to determine the second derivative of fx at x=-2 with a…

Q: 4. Compute the second derivative with respect to x of 3x³ + 8 y : at x = 1.

A:

Q: Assuming that the derivative of arcsin(x) is indeed 1/√1 − x2, supply the justification that allows…

A: Recall the power series expansion for 1/√(1 − x2) The same  can be written as: 1/√(1 − x2) = c0 +…

Q: 22 Find the 43rd derivative of (1 + x²)“ at x = 0. 0.

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Q: Find the derivative of f(x) = –4 ln (5 cos (-4x))

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Q: 1. Y= 3x -x- 2

A: Find your answer below

Q: Suppose the derivative of ƒ is ƒ'(x) = x - 3.a. Find the critical points of ƒ.b. On what intervals…

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Q: Find the derivative of flx) = x 1x \ - Does plo) exist

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Q: Find the derivative of f(x) = e" – a3 +In(x) - In(x)

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Q: Find the derivative of the function

A: We have to find the derivatives of the function: y=x tan-12x-14ln1+4x2 If two functions are in…

Q: Solve for the derivative of the function using chain rule. 8. f(x)= sin (2x)cos (3x)

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Q: Find the equation of the tangent line to the function f(x) = x² – 2 at the point (1,-1). You must e…

A: Given, fx = x4 -2  We have to find the equation of the tangent line to function at the point 1, -1.

Q: 10. Find the first derivative: f(x) = (x³ + 2x) In x %3D

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Q: Find the derivative of the function by the limit process. PX) = x - 9x + 1

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Q: Find the derivative of g(x) = e-" cos(x²)

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Q: find the derivative of y with respect to x, t, or θ, as appropriate.

A: On simplification, we get

Q: If ƒ(x) = xn, n ≥ 1, show from the definition of the derivative that ƒ'(0) = 0.

A: Now the derivative of a function f at a point 'a' is given by,

Q: 2. Find the derivative In (x+) y3=

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Q: Find the derivative of f (x) =arcoth (e³" ).

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Q: 2. Determine the 8th derivative of y with respect to x of the function f(x) = 1 + x2 and find the…

A: fx=11+x2 Differentiate the above function with respect to x. f'x=ddx11+x2=2x1+x22 Again,…

Q: Find the first derivative of h(x) if h(x) = cos (x – 2x) -

A: h(x) = cos2(x3-2x)

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln 3x + x

A:

Q: Find the derivative of f (x) = In(3x² – x)³ in two different ways; (a) with the chain rule %3D | and…

A: Given fx=ln3x2−x3aUsing Chain Rulelnfx'=1fxf'xDifferentiate w.r.t…

Q: Obtain the first derivative of the function f (x) = sinx/x using Richardson's extrapolation with h =…

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