1. Determine if the function is even or odd x*+1 g(x) = f(x) = sin x x3-2x

Q: 3. Find the derivative of the following functions: a. f(x) = (x² + 1)(x³ – 2x² – 1) f(x) = b. 2 +…

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Q: (a) Let f(x) = -3x² + 4x. Use definition of the derivative Equation 3.4 to compute f'(x). (No other…

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Q: The derivative of the function f is defined by - f'(x) = (x² + 2) sin (2x − 2). If ƒ (2) = 7, what…

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Q: Find the first derivative f' and the original function f. f"(x) = x³ – 4x + 6, f'(0) = 9, f(0) = 6…

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Q: 18 The derivative of the function f(x) = x² + is 18 4x3 + (æ³) 18 O 4x³ - (æ²) 18 4x° + (x) 4x + 18…

A: d/dx(xn)=nxn-1 Given f(x)=x4+18/x  To find the derivative of f(x) differentiate once

Q: If f'(x) = 3+ 4x and the curve f(x) passes through the point (1, 8) i) Find f(x) ii) Find the local…

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Q: Find the open intervals on which the function is increasing or decreasing.

A: Given: fx=sinx-1, 0<x<2π To Find: Increasing and decreasing function.

Q: -x² +1 Let f(x) be defined as f(x)={* - | 1–sin² x if x20 if x<0

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Q: 2. Find the derivative of (a) f(x) = x4 +2x-2 + 4ex

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Q: c) If f'(x) =3+ 4x and the curve f(x) passes through the point (1, 8) i) Find f(x) ii) Find the…

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Q: 10 Find the derivative f'(0) of f(x) = at x + 4 x = 0 using the laws of differentiation.

A: Derivative of the function

Q: 1. Find a, b, and c such that the function f(x) has a derivative at x=0 and x=2, where: tan-1(x);x…

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Q: Find the open intervals on which the function is increasing or decreasing.     f(x) = sin x − 1, 0…

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Q: Sketch the graph of the function f(x) = 12 x sin x on the interval [−3π, 3π]

A: we have to sketch the graph of the given function at the given interval. f(x)=12xsinx on the…

Q: Sketch a graph of the function f(x) = 0.5 sin(3x). 4+ 2 -5/6 -27/3 -T/2 -T/3 -Tt/6 T/2 2/3 5/6 -1 -2…

A: Here is the solution

Q: a) Let f(x)=-3x² + 4x. Use definition of the derivative Equation 3.4 to compute f'(x). (No other…

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Q: Let k(x) = tan−1 x. Find the value of k(9)(0), the 9th derivative of tan−1(x) at x = 0.

A: Given

Q: 5. Let f(x) = 5x4 -+ 8Vx - 3. x2 (a) Find f'(x). (b) Find an equation for the tangent line to the…

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Q: The derivative of the function f is defined by ƒ'(x) = (x² + 5) cos (3x). What is the x-coordinate…

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Q: 5 .Let f(x) =x² -e*. Find the value of x for which the second derivative s"»equals zero. 2

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Q: 2) a) Let f(x) = 2* + 3x7. Find f'(x) and f" (x). b) Find the derivative f'(x) in the following…

A: a.)   Given f(x) = 2x + 3x-1/2 f'(x) , f''(x) are to be calculated. Formulas used here  ** y = ax…

Q: 1. Let f(x) = Find the equation of the tangent line to the graph of f'(x) at the point x² + 1 where…

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Q: Find the equation of the tangent line to the function f(x) = In(5x) at x = 2. (Use symbolic notation…

A: Given that, f(x)=ln5x To find the equation of tangent line to the function f(x)=ln(5x) at x=2.

Q: 1-Find the first derivative of the following function f( x) 5 cos (10x) + x' – 2x – 6x+ 10 For x=2…

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Q: 4. For what values of x does the graph of f have a horizontal tangent if f(x) = V3 x – 2 sin(x).

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Q: 5. Find the requested derivative for each function, and simplify (reasonably): a) f"(x) for f(x) =…

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Q: If f (x) = sin 2x , find all of the stationary points of f (x) on 0<x<2n

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Q: Let f(x) be defined by f(x) = 3x² + 5x + 2. Find the slope of the tangent line to the curve y = f(x)…

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Q: Solve for the derivative of the given functions using the Chain Rule formula. a.) Let f(x) = √(x2 +…

A: Solution

Q: 1) Find the hundredth derivative of p (x) = (x+ x³ + x")1º (1 + x²)!' (x³ + x³ + x7). Justify your…

A: The given polynomial function is px=x+x5+x7101+x211x3+x5+x7 We have to find the hundredth derivative…

Q: 9) Find f(x) if f'(x) = 7 sin x + 2x - 3 and f(0) = -3

A: Obtain f(x) by integrating the given first derivative as follows.

Q: 1) Use the Product Rule or the Quotient Rule to find the derivative of the given function a – g(x) =…

A: The objective is to use the product rule or quotient rule to find the derivative of the given…

Q: Find the inflection points of the function f(x) = x 2 ln x

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Q: 5. Find all x-values in which your function has horizontal tangent lines, f(x) = 2 sin x + x. given…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the derivative of the function ffor n = 1, 2, 3, and 4. sin x fx) = - (X), I n =4 Use the…

A: Solve for the derivative

Q: 9x Find the derivative of the function f(x)=In x2+15 2x O f'(x)= x²+15 15-x2 f"(x)= x2+15 2x O…

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Q: 1. Compute the first, second, and third derivative of a. f(x) = x² In(x+1) b. h(x) = x² sin x

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Q: Find the function f(x) whose derivatives is sin x and whose graph passes through the point (0,2). O…

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Q: At what other point does the tangent line drawn to the curve f (x) = x ^ 3 from (2,8) intersect?

A: Given curve is : f(x)=x3   ..............(1)           and tangent drawn from (2,8)

Q: On the graph of f(x)=sinx and the interval [0,2π), for what value of x does the graph cross the…

A: Plot the graph of sinx given below

Q: 4. If f(x) = sin x, show that f(2.x) = 2f(x)f(-x) %3D

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Q: 11. (a) Find F'(x) using the limit definition of the derivative if F(x) = F'(x) will result in zero…

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Q: 15) Determine the 3rd derivative of the function f(x) = 2\x-x³ [T:2]

A: topic - derivatives

Q: 11.Find the derivative of the functions: a) f(x) = In(9x²2 – 3x) b) g(x) = In(ln x)

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Q: 2) Find the derivative of the following func (c). f(x) = (x+ 7 sin z) (1 – 5 cos x) tanx (d). g(x) =…

A: We can find the answers as below.

Q: Prove without graphing, that the graph of the function has at least two x-intercepts in the…

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Q: 1. Find the derivative of f(x) = x² – 3x. Use the result to find the slope of the tangent line to…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find an equation of the tangent line to the graph of the following function f at the specified…

A: The given function is f(x)=4xx2-5. Find the equation of the tangent line to the graph of f(x)=4xx2-5…

Q: 5 Let f(x) =x -e*. Find the value of x for which the second derivative f“equals zero. 2

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.