Let f(x) = (x² + 3x)e*. Determine the value of the third derivative of f(x) for x = 0.

Q: Find the first derivative of g(x) = - 5 In(x)cos(r"). g'(x) =

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Q: find the derivative of the function  f(x) = e5x sec x

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Q: Find the derivative of f(x) = (3x – 2x?)’using the chain rule %3D

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Q: Find the 2nd derivative of y with respect to x : y=xe^2x

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Q: Find the derivative of the function.

A: Given: To find: Derivative

Q: Find the derivative of the function.

A: Given function is By using the properties of logarithm, ln(a/b)=ln(a)-ln(b) and ln(a^b)=bln(a), we…

Q: Find the second order derivative of f(x) exsinxcos2x

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Q: Find the thousandth derivative of  f(x)  = x e-x

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Q: Find the first derivative of g(x) = - 9e* tan(x). : (x),6

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Q: Find the derivative of k(x) = log3(x) cos

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Q: Find the derivative of the function. f(x) = In(x + 1) f'(x) =

A: To find the derivative of the function fx=lnx+1

Q: f(x) = cos (x – a -2).

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Q: y = In- e 2x+1

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Q: Find the derivative of y with respect to x. 2. y²(x + 2y) = e²

A: Given,

Q: Find the first three derivatives of y = x(In x)³

A: given problem :y=xlnx3

Q: Find the second derivative of f(x) * f(x) = cos² 7x

A: The given function is: fx=cos27x   As we know that; The Chain Rule: fgx'=f'gx·g'x The Product Rule:…

Q: f(x) = x In x

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Q: Find the second derivative of the function.     f(x) = x cos x

A: Given: fx=xcosx for finding second derivative of given function, we find first derivative then…

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

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Q: Determine the derivative of g ( x ) = 3 e-4 x*sin(7 x) with respect to x. = (x), 6

A: As per the guidelines, we need to author the 1st question.  We know that product rule is given by…

Q: Let y = x(ln x)² – 2x In x. Find the value of X for which the second derivative, y" (x), equals…

A: Solve the following

Q: 5. Find the first order derivative with respect to y of the function U = In/x² + y² + z²

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Q: Find the weak derivative of f() = |x² – x + 1/5| on the 1) interval (0,1).

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Q: Use the Chain Rule to express the second derivative of f ◦ g in terms of the first and second…

A: First, find the first derivative of the function, consider that the function f(x) and g(x) are…

Q: y = cof'/ x2-1 x²+

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Q: F(x) = "(5t - 1) dt %3D

A: We need to find the first derivative of F(x)=∫x2x(5t-1)dt. By Leibniz's integral rule,…

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

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Q: Find the 10th-order derivative of the function y=(x2+4x+1)√ex at the point x=0.

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Q: Find the derivative of the function. g(x) = 9 + In(x)

A: We have to find the derivative of : g(x)=ex29+ln(x)

Q: 4. F(x) = (1-t) dt

A: To find the first derivative

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

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Q: k(x) = x In x %3D

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Q: Find the derivative: f(x) = cos 1 + e8x 1- e6x – ebz f'(x) =

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Q: Find the derivative of h(x) = (1+ cos x)*

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

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Q: Find the second derivative of the function. f(x) = x x sin(x) %3D f "(x) - !!

A: Given:   fx=x sinx  To find: f"x=?

Q: Find the derivative of -3x f(x) = e¯* + e2x - e %3D

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Q: (a) Find the first derivative of the function y= la) with respect to x by using the chain rule.

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Q: 1. Find the first order derivative of u = x*.

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Q: Find the derivative of f(x) = ln v4 – x2 %3D

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

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Q: c. Find the derivative of y =+- et x3 cOS X 2

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Q: Find the first derivative of g(x) = 2 In(x)tan(x*). g'(æ) = %3D

A: Given that g(x) = 2ln(x) tan(x^4). Find first derivative of this function. We know that derivative…

Q: 19. Determine the derivative of f(x) = e* coshx. O a. e2x O b. ex O c. e4x O d. e5x

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Q: Determine the derivative of the function (x) = %3D 3+e3*

A: Authoring guidelines:…

Q: In x g(x) = 2

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Q: Find the first derivative of v with respect to x

A: Given,