Consider a function d(t) that represented the distance you traveled as a function of time on a car trip. a. If you found the derivative of this function at a particular point in your travel, what would it represent? b. What would the second derivative represent?

Q: Find the FIFTH DERIVATIVE Given: f (t)

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Q: Evaluate the derivative of the following functions at the given point  ƒ(r) =π r2; a = 3

A: We first find f'(r) using the exponent rule

Q: Q3\ Find the derivative of the following function by using the definition f(x) = x-1

A: Given function is fx=xx-1

Q: following

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Q: Find the derivative of the function at the given point (a) by approximating the definition of the…

A: Given: f(x)=x1x   To prove: Find the derivative of the function at the given point (a) by…

Q: 2) The amount of money (in billions of U.S. dollars) that a country spends on research and…

A: Here the amount of money that a country spend on research and development is given as a function. We…

Q: If someone now told you that the derivative (slope of the tangent line to the graph) of f(x) at x=2…

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Q: 6. h(x) = 5cos(a)

A: Given function is hx=5cosx To find: Derivative of given function. Solution: Function is hx=5cosx…

Q: Find the derivative of the following functions.

A: Derivative of a function represents rate of change of that function.

Q: find the derivative of the following functions

A: Given: hx=x-1x3+x2+x+1 To Find: To find the derivative of the given function

Q: Find, or approximate to two decimal places,the derivative of the function at the given number using…

A: The given function can be differentiated with respect to x. Here the function…

Q: In the given question as follows, find the derivative of the function. y = e√x

A: Solution: Consider the given function is: y = ex Differentiating with respect to x we have dydx =…

Q: 4. g(x) = x° · sin(x)

A: The given function is gx=x3·sinx

Q: Let f(x) = x³ – 5x. Calculate the difference quotient ƒ(2+h)-f(2) for h h = .1 h = .01 h = -.01 h =…

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Q: On the same graph of the function f(x) = e5inx - 0.5, plot the approximate second derivative of f(x)…

A: Given:-               Team A and team B are playing football against each other. x = total  goal…

Q: 45° а. с. b. d.

A: (a) From the given graph, it is the straight line that is parallel to x-axis. Therefore, the…

Q: Given the function f(z) shown, which is the graph of the derivative f'(z) ?

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Q: Q3\ Find the derivative of the following function by using the definition f(x) = X-1

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Q: Find the derivative of the function below using the definition of the derivative. f(æ) = /T– 2x

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Q: Find the derivative of the function. 1 g(x) x2 +o g'(x) =

A: Use the basic power rule of derivative and simplifie.

Q: Find the derivative of the function. 11 m n'

A: To find the derivative of the given function here we can apply the division rule of differentiation.…

Q: Find the derivative of the following functions.

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Q: find the derivative of the following functions

A: Derivative of xn is nxn-1 for n≠0. Derivative of a constant is equal to 0. One property of…

Q: Given the graph of the function above, which of the following would be the graph of the derivative…

A: Given graph is a graph of quadratic function.

Q: Choose the correct graph of the function (in blue) and its derivative (in red) below. O B. c.

A: We will use the fact that where the function has maxima and minima derivative graph will show value…

Q: Find the derivative of the function g(x)=e^x/2−x g'(x)=___

A: To find the derivative of the function gx=ex2-xg'x=?

Q: Given the graph of a function y = f(x) below, select the representation that best corresponds to the…

A: Graph of the function given,we have to find derivative of the function.

Q: Let f(x) = x – 5x. Calculate the difference quotient f(2+h)-f(2) for h = -.1 If someone now told you…

A: Given that

Q: Find the derivative of the function. h(t) • 6 +9 h'(t)

A: Quotient Rule of differentiation :ddtuv=v.dudt-u.dvdtv2. dtndt =n.tn-1 Chain Rule of differentiation…

Q: f(x) 5 1 -1

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Q: If f and g are the functions whose graphs are shown, let  u(x) = f(g(x)),   v(x) = g(f(x)), and…

A: The given graphs of f and g are

Q: Find the derivative of the following functions.

A: Find the derivative of the following functions.

Q: Use the alternative form of the derivative to find the derivative of the function below at x = c (if…

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Q: f(x) =

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Q: 5e* Find the derivative of f (x) Зех+1

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Q: Find the derivative of the following function. x* +7 h(x) = 2x -7 h'(x) =

A: We differentiate  the above function.

Q: I. Find the derivative of the following functions. 5. f(x) = 5* x5

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Q: (b) Find and simplify the derivative of the function f(x) = /

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Q: Suppose f(x)= √1 − 3x a. Use the definition of derivative to find the slope of the tangent line to…

A: Given: f(x)= √1 − 3x To find: a. Use the definition of derivative to find the slope of the tangent…

Q: Find the derivative. F'(x) if F(x) = (e×" + 1) °

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Q: Find the derivative of the function. f(t) = arccsc(-1²)

A: Given: f(t)=arccsc(-t2) The derivative is: d(f(t))dt=d(arccsc(-t2))dt…

Q: Find the derivative of the following function. f(x) = 14 f'(x) =

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Q: Find the derivative of the following functions at a given point x= a (g) f(x)=- a=4.

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Q: Find the following derivative 1 g(x) = 2* · (x² + 1)

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Q: se the definition of the derivative to find the derivative of: f(t) = -4 – 2t. (t) =

A: Topic:- derivatives

Q: Use the alternative form of the derivative to find the derivative of the function below at x = c (if…

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Q: Find the derivative of the following function. 8x +1 h(x) = X +7

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Q: The graph of a function is shown together with the tangent line at a point P. y 5 4 3 2 1 2 3 4 6. 7…

A: topic- tangent

Q: (a) Find the derivative of the function f(x) = ex-1

A: Note: As per company policy we are supposed to solve only one question. So, kindly repost other…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: