If f'(x) and g'(x) exist and f'(x) > g (x) for all real x, then the graph of y = f(x) and the graph of y = g(x) A ) intersect exactly once. B) intersect no more than once. do not intersect. D could intersect more than once.

Q: Find derivative of 2x^4y^3-xy^2 using chain rule.

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Q: Find the derivative of the function using Chain Rule. h(x) = (2x-6)-¹ (x²+3)

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Q: Find the derivative of f(x) = (6x² + 6x – 4)arctan x 12x+6 бх2+бх-4 1 (6x2 + 6x – 4)aretan x…

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Q: Find the derivative of the function.

A: Use the chain and quotient rule of derivative to differentiate the function.

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A: For local maxima or minima:The first derivative test is f'(x) = 0The second derivative test…

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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: 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: 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: Let f(x)=," 1 Use the definition (first principle) to determine the 1-x derivative of ƒ(x).

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Q: find the derivative of f(x) = (x²+4)(3x³ - 2x) at the point x = - 3[ use product rule] %3D B.

A: We have to find the derivative

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A: Critical points are points where the function is defined and its derivative is zero or…

Q: 2. Find the derivative of f'(x) if ƒ(x) = x*+3x-V x2+x

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Q: 7) f(x) = 3e In x %3D

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Q: use the first derivative test to characterize each critical value of f(x)=x3+6x2-18x+3 as a maximum,…

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Q: Find the derivative of f (x) = 9x − 5 at x = 2 and x = 5.

A: The derivative of a function f(x)  at a point a  can be calculated by applying the value a   to the…

Q: Find the first derivative: y= In V5x3 - 2

A: Given: y=ln5x3-25 We need to evaluate dy/dx. This can be done as follows:

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: 1.f(0) = (금x* + 3)" %3D

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Q: Find the derivative of the function using Chain Rule. (2x-6)-¹ (x²+3) h(x)=

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Q: =) f(x) = x²e¬4x

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Q: 3) Find the derivative f(x) = xe-*In(x³) %3D

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Q: Determine the derivative of the following functions using chain rule. 3 * 1. f (x) = (2x² – 2x + 1)…

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A: Consider the given function as y=xtan-12x-14ln1+4x2

Q: What is the derivative of the function r (x) 5 (9x²-2) (5x+7) (3x³-2x+2) 9x²-2 5 5x+7 3x³-2x+2 5…

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Q: Where does the derivative of g(x)=(x^2)/((x^2)+3) = 0 or is undefined?

A: Given function, gx=x2x2+3

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Q: Find the local minimum and local maximum values of the function g(x) = 6x2− 4x3 using both the First…

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A: Given function is fx=6x2+6x-4tan-1x. To find derivative of the given function. Solution: Given…

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Q: 1 3. f(x) = (-x4-3)2

A: Solve for the derivative

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A: Derivative Question

Q: Find the derivative and state the domain of f(x) = In(x + 4) %3D

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Q: Find the derivative of f(x) = arctan x In(6x? + 6x – 4) - 12x 1 1 In(arctan(x)) + In(6x² + 6x – 4)-…

A: The given function is fx=arctanxln6x2+6x-4

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

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Q: Find the derivative of f(x) = arctan x In(6x? + 6x – 4) 1 1 -In(бx? + бх — 4) + arctan x- -(12x + 6)…

A: Product rule (u v )' = u ' v + u v' Formula derivative of xn=n xn-1 Derivative of arctan…

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Q: Find the second derivative of the implicitly defined function x2+y2=R2 (canonical equation of a…

A: Given function is Differentiating both sides with respect to x, we get

Q: -f(x)=√√5x² +2

A: Please see the answer below.

Q: Find the derivative of the function.

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Q: Find the derivative of the function. f(x) = 2x In 2x %3D

A: Given, f(x)=2xln2x To find the derivative of f(x).

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A: Here the given function fx=tan-1x ln6x2+6x-4