Evaluate the 3rd derivative of M with respect to (x) M= x6 y3 Cos (x6 y3) if x =6 and y= 3

Q: f(x) = acos(b\x) x2 COS

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

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Q: Evaluate the derivative of y = cos '2x - In 1-4x, where x = 0.125 -12> 2

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Q: In xy = x² + sin xy

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Q: 5. Find the derivative of: a. f(x) = cos(e³x-4)

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Q: 2. x² + 4xy + y² = 1

A: Differentiation

Q: Find the derivative of: 9e 7sin ( 3x*) Use e^x for e". -

A: We use chain rule to find the derivative.

Q: compute the derivative y = sin(2x) cos2 x

A: Given y=sin(2x)cos2x The product rule of derivative is given by:

Q: 4) Find the derivative of the function: x* cos x h(x) %3D Vx2 + 1

A: Answer

Q: 2х- 3 3. У3 5x +1

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Q: 10. f(x) = cos (2x)e*²-1

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Q: compute the derivative. y = sin(2x) cos2 x

A: We can find the derivative of this function by using the product rule of differentiation . According…

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: Find the derivative of (a) (교2 + 1)" (6) In(cos²(e2")) 2x (c) sin-1 e-1 dt x +1 In a

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

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Q: Compute the second derivative of sin(g(x)) at x = 2, assuming that g(2) = π/4 , g'(2) = 5, and g"(2)…

A: singx

Q: Determine the first derivative of the ff. function y = Vxe2* cos x

A: Derivative of a function gives the tangent of the curve at a given point. Derivatives are used to…

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = (x2 ln x)4

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Q: 6. Find the first order derivative with respect to z of the function u = In/x2 + y2 +z²

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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: In 2x y = - cos x

A: ddxln 2xcos x= ddxln 2x . cos x - ln 2x.ddxcos xcos2 x= 12x. 2. cos x - ln 2x.(-sin x)cos2x= cos xx…

Q: Find the 25th derivative of g (0) = cos(40 + a) where a is a real valued constant.

A: The given function is: g(θ)=cos(4θ+α)

Q: Shows the derivative function of: u³ + 2u, where u = x² + 3

A: Let's find.

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: Find the derivative: 1+ e2x = cos 1 - e6x f(x) f'(x) =

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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 derivative of y with respect to x. 1, 1+x2 In 1- x3 y

A: If you have function f(x) in the numerator and the function g(x) in the denominator, then the…

Q: ) .3 Find the derivative of h(x) = cos (2x – 5 %3D

A: Given,            hx=cos42x3-5To find : The derivative of the given function.

Q: Find the derivative of the function: f(x) = [sin(4x + x)] [cos(x4 + 4)] f(x) = e3x²+*(cscx + secx)2…

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

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Q: Find the derivative of the function y=cos(3 In x).

A: Given y=cos(3lnx)

Q: y = cof'/ x2-1 x²+

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Q: Compute the second derivative of sin(g(x)) at x = 2, assuming that g(2) = 4, 8'(2) = 5, and g"(2) =…

A: Given: The function singx with g2=π4, g'2=5, and g''2=3, To find: The second derivative of given…

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

A: Given problem:- Solve for the derivative of the function using chain rule.   8.     f(x)= sin…

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

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Q: Find the derivative of y with respect to x if y = (5x2 – 10x + 10) e - 6x y' =

A: We have to find the derivative of y with respect to x.

Q: Find the indicated derivative. dz x2 for z = x2 - dx 1- x - 5x2

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Q: Find the derivative of both a and b a. x csc-1(1/x) b.(esin2x)/[In(cos2x)]2

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Q: Use your knowledge on Higher-order derivative and Chain Rule to show that z" + 4z' + 8z = 0 if z =…

A: Show that, z''+4z'+8z=0 if z=e-2xsin2x+cos2x Formulas used:…

Q: What is the first derivative of g(x) = ln #*+1? x2

A: Derivative of ln(x):       ddx(ln(x))=1x Division rule of derivative:-…

Q: (x² +SJ° In 14-X つ. dr

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

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

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Q: Find the derivative of y with respect to x for y = (- 7x2 – 5x + 5) (sin x + 11x) 1x + ..... The…

A: Given:- y = (-7x2-5x+5) (sin(x) +11x)  To find:- Derivative of y

Q: -5

A:

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 first derivative of v with respect to x

A: Given,