1 Differentiation of a complex function dw =f'(z)%3 Lim Sf(Zo+8z) – f(zo) Sz w =f(z) dz 8z-0

Q: dy dx (b) y = (x³ - 2x + 8) (x² + 4) 1. Use the Differentiation Rules to find (a) y = 6x³ + 3x√x -…

A: Since you have posted a multiple question according to guildlines I will solve first(Q1)   question…

Q: Find an equation of the tangent line to the graph of the equation at the given point. x² + x arctan…

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Q: QI @ Find fx and fy for the following function: (i) f(x,y)=(x²-1)(y + 2) (ii) f(x,y)= ex+y+1 (iii)…

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Q: diffelentiate y= In(登) 2X 3.

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Q: Find y' by implicit dif ferentiation for 2y³+4x² –y = x6 . 6x5- 8x y '=- 6y2 – 1 A 6r5 + 8x B 6y2– 1…

A: Given, 2y3+4x2-y =x6 We have to find y' by using the implicit differentiation.

Q: 1. Find y' by implicit differėntiation. xy + 4x + 5x² = 3 %3D Select the correct answer: a. y':…

A: In implicit differentiation write y' interns of x & y.

Q: Find the derivative of y with respect to x using implicit differentiation in the equation *³y =…

A: We can find the derivative as below.

Q: What is the gradient of the function f(x) = 5 sin(5x) A sin(5x) - sin(5x) E B 25 cos(5x) F -cos(5x)…

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Q: Find the derivative of this complex equation using logarithmic differentiation?

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Q: dy Evaluate dx at point (4,2) given 3(x² + y²)² = 100(x² – y²).

A: Answer and explanation is given below

Q: lanarithmic differentiation bo find desivative of the function. (x+)"(x-s y= (x-3).

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Q: 6z²–2z Find the derivative of f(z) = " z + 0 . Select one: 6z-12 O f'(z) = O f'(z) = 6–12z %3D 6–2z…

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Q: 19.3. (a) Using the chain rule, find ðf/ðz* and df/dz in terms of partial derivatives with respect…

A: We use chain rule

Q: ax +b 35. y= cx+d 36. y= (x' +4x) 37. y = (r -x+1)

A: 35 Given function is y=ax+bcx+d. Differentiate y=ax+bcx+d with respect to x, we get…

Q: x f(x) f'(x) g(x) g'(x) 34 1 6 1 4 -2 -6 1 3 5 1 3 3 6 5 1 3 -2 4 The functions f and g have…

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Q: (i) Find af/Əx, and f/ayəx of the following functions. (a) f(xy) = x?y + x³y? (b) f(x,y) = 10x + In…

A: Partial differentiating f(x, y)  first order and second order

Q: QI// Find the first derivative for the following functions: (*+1)(x +2) (x-1)(x 2) r'+ 3e *2 2) y -…

A: NOTE*** As per bartleby guidelines for more than one question asked only first to be answered, send…

Q: Given f"(x) = - (2æ³ + æ² + 8x + 6), f'(1) = –7, and f(1) = 2. Find f'(x) and f(x). Part 1: Find the…

A: To solve the following problem

Q: Find an equation of the tangent line to the graph of the equation at the given point. x² + x arctan…

A: The point on the curve through which tangent passes is, .The slope of the tangent is given by, The…