Let P(x) = F(x)G(x) and Q(x) = F(x)/G(x), where F and G are the functions whose graphs are shown F G (a) Find P '(2). (b) Find Q'(7).

Q: Compute the derivative of g(x)=arctan(x^3+1)

A: From the given data:

Q: i. y= ) In (x+3

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Q: Find the derivative using the chain rule: x(x^2+1)^(-1/2)

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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: Find the derivative of the function.…

A: The given function is hx=x2arctan8x

Q: find the derivative of y with respect to the appropriatevariable. y = ln (x2 + 4) - x tan-1 ( x/2)

A: We use the chain rule and product rule

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: The derivative of f(x) = 5x – Vx + (sin)x – e² -

A: Given; f(x)=5x4-x1/3+[sin(π/2)]x-e2

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

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Q: x + x dx x2

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Q: 1. Find the first derivative by using the definition for f(x) = 3x² – 2x – 5, hence - find f'(-2)

A: Derivative of a function is ratio of difference in output and difference in input.

Q: Find the derivative of the function y = arctan x + x 1+x²

A: Given: y=arctanx+x1+x2Recall the formulas:ddxarctanx=11+x2     ..........1ddxuv=vdudx-udvdxv2…

Q: 10. f(x) = cos (2x)e*²-1

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Q: 2) Use the Chain Rule to express the second derivative of fog in terms of the first and second…

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Q: 2) Find the derivative of the function f(x) = (x³ – tan(4x² – 2)* |

A: Given :            To find the derivative of the given function                f(x) = x3 -…

Q: 2х Find the second orfer derivatives of y=Tan" 1-x3

A:

Q: Find a function y=f(x) whose second derivative is y''=12x-2 at each point (x,y) on its graph y=-x+5…

A: The second derivative of the function, y and tangent to the graph of y is given as,

Q: (b) Use implicit differentiation by partial derivative to solve for of function 3x2 + 2xy = -4y3. dx

A:

Q: Find sixth order derivative of the function f(x)=(x-5)^7.cos(5x) by using Leibnitz theorem.

A: n! = n × (n-1) × (n-2) × (n-3) × (n-4) × ............ × 1

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: 3) Find the first derivative of y=(In x)"

A: According to our guideline 3 subparts of question or the first question can be answered and rest of…

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

A:

Q: Find the derivative of the function. h(x) = x² arctan(8x) %3D

A: To find the derivative of hx=x2tan-18x

Q: 5. Find the derivative of y = In(cos v3x + 2 ), by using chain Rule.

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Q: Find the derivative of the function y= arctan x +x/1+x2

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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 f(x) = –4 ln (5 cos (-4x))

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Q: Two equivalent forms of the Chain Rule for calculating the derivative of y = ƒ(g(x)) are presented…

A: Two equivalent forms of the Chain Rule for calculating the derivative of y = ƒ(g(x)) are presented…

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: Calculate the first derivatives of ƒ(x) = x2/(x2 + 1) and g(x) = -1/(x2 + 1). What can you conclude…

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

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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 indicated derivative. dz x2 for z = x2 - dx 1- x - 5x2

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

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Q: 4) Find the derivative of y = arctan(x² + 3)

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Q: I FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORM х 1. y= Arctan- 3-V9-x²

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 2) Use the Chain Rule to express the second derivative of ƒ • g in terms of the first and second…

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Q: Find the derivative of the function by the limit process. f(x) = x3 - 9x + 1 f'(x)

A: We know,f'(x) = limh→0 f(x+h) - f(x)h  by limit processHere,f(x) = x3 - 9x + 1So,f(x+h) = (x+h)3 -…

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: 2) Use the Chain Rule to express the second derivative of ƒog in terms of the first and second…

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Q: 5. Find derivative of the following composite function using the Chain Rule: f(x) = 3x2 + 8x, x(t) =…

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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 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: Find the derivative of y = arccos x + x 1-x²

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Q: 1.Find the derivative of y = - arcsin %3D V4-x2

A: Given:        y=x4-x2-arcsinx2 differentiating on both sides     dydx=ddxx4-x2-arcsinx2…