For the function f(x) =-X find f"(X), f"(0), f’"(1), and f"(- 1). "(X) = O I7

Q: Find the first and second derivatives of the function. f(x) = In(x + 4) f'(x) = f"(x) I3D

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

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Q: Solve for the derivative of x² – y² = 9 using implicit differentiation %3D

A: Given :                x2 - y2 = 9To find :                 y'

Q: Find the 1st derivative: Complete Solution.  y=2cos2 t/2

A: y=2cos2 t/2

Q: What is the critical point of the function f (x) = cos x?

A: what is the critical point of f(x)=cos(x)? for critical point, f'(x)=0

Q: Find the derivative of f(z) = e2" (3z2- z)

A: Given, f(x)=e2x(3x2-x) Here, when we try to find the derivative of f(x), both chain rule and…

Q: Find y" by implicit differentiation. 3x3 + 5y3 = 7 y" II

A: Given       3x3+5y3=7   1using implicit differentiation, w.r.t x1  ddx(3x3) +ddx(5y3)=ddx(7)…

Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – /cos(x) At the point (, (2n…

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Q: Use the chain rule to find the derivative of the function z = x2y3 − x along the curve given by x =…

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Q: Solve for the derivative of the Hyperbolic Differentiation. 1. y = ex cos h 2x 2. y = ln sin h x…

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Q: Find the differential of the function y = x- sin x.

A: Given: y=x2-sinx

Q: Find  y''  by implicit differentiation. 4x2 + y2 = 4

A: Given,  4x2+y2=y,we have to find y''Differentiate with respect to x,we get…

Q: Calculate differential: f (x) = = e-* cos(3x) + 2 of the range [1,2] with h=0.05 a) Using the…

A: Equation is f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of the…

Q: Find the global maximum and minimum of the function on the given…

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Q: Find by implicit differentiation for x2+y2=25 at point P(0,5).

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

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Q: 3x V1-x x = 0. y(x) = at Equation of the tangent line

A: Given,           yx=3x1-x2 at x=0

Q: Compute the derivative using derivative rules.

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Q: find derivative of the U function 1-x f(x) = sec-1. 1+ x ーオ

A: Explanation of the answer is as follows

Q: Find  y ″  by implicit differentiation. 4x3 − 5y3 = 8

A: First we find y' by differentiating  both sides of the given equation. Then find y"  by using the…

Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – cos(x) 2n 4+v3 3' 23 At the…

A: Answer

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

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Q: Find the derivative and simplify exy -x² = 4Y² %3D

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Q: 9. For f(x) = arctan (2 sin ( Vx )) , compute the first derivative at the point %3D X =

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Q: Find the derivative of the function using chain rule. f(x) = esin?x

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Q: Find the derivative of the function. f(x) = 18 In(x) %3D

A: Derivative Question

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: Find the critical value of f (x) = vx² + x – x using the second derivative test. %3D

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Q: Calculate differential: f(x) = e-* cos(3x) + 2 of the range [1,2] with h=0.05 Using the backward…

A: Equation is  f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of…

Q: 3. ƒ : R+ → R, such that f(x) = √2x+2. (Hint: Apply the chain rule.)

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Q: For a function f (x, y), (0, 0) and (1, 1) are two critical points. Also, fxx = 2x², fyy = y²2 and…

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Q: Find the derivative of the function. InV y = In 6 - X %3D y' = %3D

A: Explanation of the answer is as follows

Q: Find the differential of the function.

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

Q: B) Find the derivative of the foiiowing: 1) y = 2sin2(5x) ,2) y = x, 3) xsin-14y = y tan-14x 4) y =…

A: As per the company  guidelines we have to solv first 3 subparts if suborats are not mentioned  So…

Q: Find the linear approximation of the function f (x,y) = ln (x - 3y) at point (7,2).

A: To find the linear approximation of the function fx, y=lnx-3y at the point 7, 2.

Q: the Chain Rule.

A: Given: y=11-x46. Let, u=1-x4 By chain rule, the derivative of y with respect to x is given as,…

Q: If f(x,y) is a real valued function of two variables then what is the second derivative of f?

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Q: 23-4z2-2一4 y = %3D 1+ Va

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Q: (a) By using the chain rule and the derivative (1, if x>0 4 (1xl) ={-1, if x<0 %3D find (lx-x) vxE…

A: Use the chain rule to differentiate the above given function and than use the given derivative of…

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: Find sixth order derivative of the function f(x) = (x – 5)7.cos(5x) by using %3D Leibnitz theorem.

A: If y=uv where, u and v are functions of x then un and vn denote the nth derivative of u and v with…

Q: Determine the n-th derivative fn) of the function f: (0, +0) → R, f(x) = x ' exp ( 1 - ), n EN

A: f(x)=1x,  f:(0, +∞)→R,…

Q: Find the derivative of y with respect to x. 6x + 7 -1 6. y3-Cos %3D

A: dydx=?

Q: Find y'' by implicit differentiation 4x3+3y3=6

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Q: Find y(1) for y" = - 4z - 4y, X, = 0, yo = 0, z, = 1, with step length 0.1 using Euler method (2nd…

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Q: Using the đết of derivative, fin rivative of f(x) = x² + 2x + 2.

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Q: Find y" by implicit differentiation. 9x2 + y2 = 4 y" = %3D

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Q: r(x)= cos (3x)

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