F1 (mi/gal) 30 + 20 + 10 +++ + 10 20 30 40 50 60 70 v (mi/h)

Q: Explain how the first derivative of a function determines where the function is increasing and…

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Q: 1. Can the graph of a function have more than one tangent at a given point? Explain by giving an…

A: Query- Can the  graph of a function have more than one tangent? Explain by giving an example and…

Q: 1/x using the definition o

A: we have to find the derivative of f(x) using the first principal. f(x)=x+1x

Q: How do you find the fifth derivative of a function?

A: To find the derivative we differentiate the function once.  To find the second derivative we…

Q: What is the meaning of a derivative?

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Q: 45. y = cos vsin(tan x)

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Q: Find the slope of the graph of the function at the given point. Use the derivative feature of…

A: f(θ) = 4 sin(θ) - θDifferentiating, we get  f'(θ) = 4 cos(θ) - 1 f'(0) = 4 cos(0) - 1 = 4 - 1 = 3y -…

Q: Find the derivative of the function. y = sec 2  x  +tan 2 x

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Q: Define the second derivative of f. If f(t) is the position  function of a particle, how can you…

A: Second derivative is derivative of the derivative.      Therefore,…

Q: True or false? A function does not have a derivative at x if its left hand derivative is not equal…

A: True or false for the given statement A function does not have a derivative at x if it's left hand…

Q: a.) A sphere shaped balloon is being inflated with a rate of 800 cm³ per minute. When the radius of…

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Q: Find the derivative of the function. y- tan-(V-8

A: In this question, we need to calculate the derivative of the given function.

Q: Find the derivative of the function 3 tan (x- 2 1 x y

A: Given:

Q: How do you find the derivative of a constant multiplied by afunction?

A: If f(x) is any function and let y=cf(x)            function f(x) multiplyed with a constant, c is…

Q: What is the derivative of the following function

A: Given that: 1. h(y)=y1-ey2. f(t)=1+5tln(t)

Q: The equation of a curve is given by f(x) = √2x-1. a) Use the definition of derivative to find f'(x).…

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Q: Match the graph of the function with the graph of its derivative.

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Q: 4 -4 -3 2 4 -2

A: See from the given graph of the function fx, the graph becomes parallel to x axis at the points x=-2…

Q: cosx y =-

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Q: How do you find the derivative of (tan(x)-4)/sec(x)?

A: Use the quotient rule to find the derivative of (tan(x) – 4)/sec(x) as follows.

Q: ■ Find the derivative of the function. Simplify wherepossible.  y =  ( tan -1 x ) 2

A: y=tan-1x2

Q: What is the derivative of a constant function?

A: The derivative of constant function is always zero.

Q: Find the derivative of the function using the definition of derivative. f(x) = x4 f'(x) = %3D

A: To find the derivative of the given function using the definition of derivative.

Q: Explain the relationship between the slope and the derivative of ƒ(x) at x = a.

A: Given function is  fx at x=a

Q: 6. Sketch the graph of y= x2+ by using the properties of the derivative.

A: The given function y=x2+2x

Q: explain to me details what is Distinguish Between Partial Derivative and Ordinary Derivative ?

A: Given

Q: Find the second derivative of the function.

A: Given,         f(θ)=3tanθ

Q: 5. What is the definition of the derivative of a function f(x) ?

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Q: How do you find the derivative of f(x)= sec(x)tan(x)?

A: Some properties of derivatives:Following are some of general derivatives and derivatives of…

Q: find the derivative of the function f(x) = x2 what is f'(3)? what is the equation of the line…

A: Given function is f(x)=x2

Q: 3. Give the definition of a derivative of a function f of one variable at a point xo. /2 Find the…

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Q: How do you find the derivative of the quotient of two functionsthat are differentiable at a point?

A: Given: Let f and g be two differentiable function at point x.

Q: Enumerate and explain the steps in finding the derivative of this function: y=1/[2*sqrt(x+3)]

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Q: Find the second derivative of the function. f(x) = sec x * "(x) = Noc

A: Please see the explanation below

Q: . What process can you use to find the derivative of f(x) g(x) ? Illustrate by showing how to take…

A: We have to find

Q: how to find the derivative of 1-sec x

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Q: How do you find the derivative of the product of two functionsthat are differentiable at a point?

A: Consider the two functions f(x) and g(x). f(x)·g(x)'=f'(x)g(x)+g'(x)f(x). Here f(x)·g(x)' represents…

Q: 14. Find the derivative of the function using the definition of derivative. f (x) = V1 – x

A: Derivatives

Q: Illustrate the Derivative of Cosecant Function ?

A: Illustrate the Derivative of the Cosecant Function?

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

A: Given function is, f(x)=tanx.

Q: 5+x f(x) = 3—х

A: Solve the following

Q: How do you find the derivative of function y=x^2-2radicalx/x

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Q: 10

A: The graph of derivative is made by observing the slope of given function

Q: What is the derivative of: y = x√arcsin x

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Q: The derivative of a function is f '(x) = x2(x + 4). At what value(s) of x does f have a horizontal…

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Q: State the notation/symbol for: derivative of y with respect to x derivative of f(x) second…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 5. Find the 25" derivative of y= In x.

A: We have to find the 25th derivative of y=ln(x)

Q: What do you look for when you need to match the graph of a function with the graph of its…

A: Observe the behavior of graph as the value of x increases.

Q: Determine the sign of the second derivative function as x varies. Where is f' positive? Where is…

A: Let's draw the graph of f''(x).