If the sign of the first derivative function is positive, the main function f(x) is decreasing.

Q: Sketch the graphs of two functions that have the given derivative: f'(x)=2

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Q: y = 4x° + 4x at (1, 2)

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Q: What is the derivative of the function f(x) = 2x + 3 at the number x = 4?

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Q: Find the derivative of the function g(x) = sech2 3x

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Q: What is the derivative of y= 2^x + x^2 / x-3

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Q: Find the first and second derivative of 2 X + 3 3 x' x X y 4 +

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Q: Find the derivative of the function. 5 F(x) 1 + 4x + x3 F'(x) :

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Q: In(x²) What is the derivative of

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Q: Why is the derivative of a constant function zero?

A: Consider the constant function fx=k. Apply the derivative definition as follows.

Q: Find the second derivative of the function.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the derivative of the function. X-1

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Q: Find the derivative of f(x) = 10/x

A: We can find the derivative as below

Q: Find the derivative of the function f(x) = 4x

A: The given function is f(x) = 4x Formula used ddx(ax)=axln(a)

Q: Here is the graph of the second derivative of a function g(x). g"(x) Where does g(x) have a point of…

A: Inflection point is at that x value where the double derivative of the function is 0.

Q: Find all functions ƒ whose derivative is ƒ'(x) = x + 1.

A: Given that f'(x)=x+1

Q: Find the derivative of y = x*. .5"

A: Given that: y=x5x

Q: Suppose that the second derivative of the function y=f(x) is y'' = (x-3)(x+9). For what x-values…

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Q: Find the derivative of function (x+2)² (x – 1)3* f(x) -

A: f(x) = x+22x-13f'(x) = x-13×2x-2-x+223(x-1)2x-16f'(x) = x-12x+22x-1-3x+2x-14f'(x) = x+22x-2-3x-6x-14

Q: find the derivative of the function F(x)=4(x^3-x)^4

A: According to the given information, it is required to find the derivative of the given function.

Q: If f(x) = e cosT, the second derivative f"(x) is:

A: The given function is fx=ex cosx. Evaluate the first derivative of the given function as follows.…

Q: Find the derivative of the function f(x)=x-2/2+x square root

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Q: Find first and second derivative of y=x(x-4)^3

A: Given function is  y=xx-43 To find derivative product rule is used duvdx=vdudx+udvdx So the first…

Q: Find a function whose square plus the square of its derivative is 1.

A: To Find a function whose square plus the square of its derivative is 1.

Q: How can the derivative function definition be applied to this problem?

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Q: Give a nonzero function that is its own derivative

A: Consider the function fx=ex.

Q: 1, Find the first and the second derivative of f(x): f(x)=x

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Q: find the derivative of y if X(メ+リ(メ-2) (x)くメ+3)

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Q: Determine the value of X on which the derivative of the function Y = | 3x² + 4x + 1] does not exist.

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Q: If y=Incscx, then the value of first derivative (y) is

A: The given function is y=ln cscx.

Q: If a function is decreasing with an upward concavity, what do you know about the function's first…

A: Given :   If a function is decreasing with an upward concavity To find : the function's first two…

Q: Find the first and second derivative if w = 3z-2-(1/z)

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Q: What rule should be used in getting the derivative of y=(1−x^2 )^6

A: What rule should be used in getting the derivative of y=(1−x^2 )^6

Q: Find the second derivative of f(x)=x4.

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Q: Find the derivative of the function.    y = x/√(x4 + 4)

A: The given function is , y=xx4+4 To find the derivative for the given function. Solution: The given…

Q: If f(x)=4sinx-x^3, what is the second derivative of f?

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Q: If f(x) = x-2 x² +4 then what is the derivative of fat x=2?

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Q: Evaluate the second derivative of the function below at (1, -2). y² = x³ = x + 1 -

A: To evaluate the second derivative of the function at the given point.

Q: Find the Derivative Function, f(x)=1/7x7-1/3x4

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Q: Find the derivative of the function. y= 2^(3-x^2)

A: Given function

Q: Determine the value of X on which the derivative of the function y 3x2 + 4x + 1| does not exist.

A: Giveny=|3x2+4x+1|y=|3x2+3x+x+1|y=|3x(x+1)+x+1|y=|(3x+1)(x+1)|Using modulus propertyy=|3x+1||x+1|

Q: If fox) is odd function , then the derivative of y =coshf(-x)) equals

A: here option B is true

Q: 4. f(x)=

A: The given function is: fx=5x2x+3   As we know that; The Power Law: ddxxn=nxn-1 The Quotient rule:…

Q: Find the second derivative of f(x)=x(x^2+1)^3

A: Find the derivative of function:

Q: If the function of x, ƒ(x) = · then, the derivative of f(x) is:

A: We will find the derivative of f(x) as following

Q: Find the derivative of y= (x+2)x+2

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Q: 7. If h(x)=|2x- 3, what is the value of the derivative at x = -2?

A: According to the problem we have

Q: If y=x+ 4÷x+1 use the first derivative test to find where relative extrema occur.

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Q: Suppose the first derivative of a function is f'(x) = (x- 30)(19x+ 1). The function f is decreasing…

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Q: The first derivative of the function f(x) is given by its graph.. f'(x) 3- 2-

A: A.  Function is increasing when f'(x) > 0  from graph  Function is increasing…