14 Consider the following two functions: 1 exp dx %3D (面) e() tan (2) %3D Explain why both of these functions fit the requirements of a sigmoid function. Ho these two functions differ from each other?

Q: ind the derivative. FA h Cx) = 2. (5x*+4

A: To find  The derivative of h(x)

Q: Find the second derivative of the function. 20 (2-0) 20 dr 2 O A. do 2 1 B. do? O OC. do 1 OD. do?

A: Given:  A function is given by,r=1+2θ2θ2-θ To Find: The second derivative of the given function…

Q: Based on Degree two function: V x (V f) = ? О 1

A: Answer: None of these.

Q: Differentiate the following function.   y = ln(9x)

A: Consider the following function:      y=ln(9x) Find the derivative of the tunction.

Q: 4 2 1 To find the blue shaded area above, we would calculate: f(x)dx = area Where: a =| -3 X, b = 3…

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Q: Differentiate the following functions. y = tan x

A: y=tanxwe know that tanx=sinxcosxy=sinxcosxdifferentiate both side with repect to x by using quotient…

Q: ə e(g?+5xy-24 +4) dx x(2x + 2y -1) dly + メ

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Q: 1. Find the general solution of 2 ylnx dx = (x+¹) ²

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Q: Evaluate the function shown

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Q: (х + 1)e* 45. g(x) %3D х — 2

A: (45). g(x)=(x+1)exx-2

Q: (a) f(x) = 2x7 – 3x4 – 41x? – 73 (b) f(x) = x cos x

A:

Q: Зх-1 -dx 2 x+1

A: Given query is to find the integral.

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A: In this question we have to find the equation of the line tangent to the graph of f at the indicated…

Q: 1. Find f* dx by hand and show how to check the result is correct by differentiation.

A:

Q: Differentiate the following function. You do not need to simplify the derivative. g(x) = – 3 + 12e9…

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Q: The derivative of the function is equal to Select one: O a.e (2* In 2) b. e* (2* In 2 + 1) c. x(2*…

A: Given function is By using the law of exponents x^m/x^n=x^(m-n), we get Differentiating with…

Q: Use the table to the right to find the given derivative. 2 3 4 f(x) f'(x) 3 1 4 2 d xf(x)] 2 3 4 dx…

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Q: 3 4 1 To find the blue shaded area above, we would calculate: f(x)dx = area a Where: a = f(x) area

A: We will use concept of integration to solve this.

Q: Differentiate the Following Function   y = ln(x)/x^2

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Q: Determine the following indefinite 12 dx X 12 dx = X

A: The given integration is ∫1-x12xdx.

Q: Suppose that is a testing function Then Ax)&(2x-3)dx is equal to 3 Oa Ocj42) e No correct answer 3/2

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Q: e2x-e-2x 4. y= e2x+e-2x

A: Hyperbolic functions are similar to trigonometric if we consider the derivatives even though…

Q: Clearly explain why the following equation is true or false. f(x) dx S FEx) dx lim

A: When the range of integration is not finite then the integral falls under improper integral.  Hence…

Q: The next step is to find du = g'(x) dx. First find g'(x). %3D g(x) = x° + 8x g'(x) = Therefore, we…

A: We can find the required answer in the following steps

Q: Differentiate the following function.   y = x/ln x

A: Consider a function y is defined as, y=fxgx The derivative of the function is defined as,…

Q: 2. Consider the following function: f(x) : derivatives. Make sure you simplify your answers. х Find…

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Q: 5) Use the table given to compute the following derivatives. 1 2 3 4 f(x) 1 f'(x) 3 -5 -9 -10 g(x) 4…

A: topic. - functions and derivatives

Q: Differentiate the following equation.  f(x)= (ln x)3 ex

A: Given:- f(x) = (ln(x))3 ex  To find :- Differentiate the given function f(x)

Q: Use the table to the right to find the given derivative. 1 2 3 4 f(x) 1 3 4 d f'(x) 3 1 4 2 dx

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Q: Differentiate G(x) =lin[e^x÷1+e^x]

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Q: Differentiate the following function: (e-*) * y = sec

A: Given: y=sece-x2

Q: Use the DEFINITION OF A DERIVATIVE to find the derivative of the function. Worth 2 questions. 8 8)…

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Q: 1. у %3D 4Сot (3 — 2х) |

A: Pls find the solution.

Q: y = ln (xm=)

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

Q: Find of the following implicit functions, where a, b and c are constant. a) ecosy = x³ sin y

A: According to our terms and condition i have solved first question for next question repost

Q: Consider the following. 7x2 - y3 = (a) Find y' by implicit differentiation. y' = (b) Solve the…

A: we have to find the derivative of the given y

Q: Differentiate the following. 4. 11 y cosec (sec x') 43 tranh2x

A: We need to differentiate the above two expressions with respect to x.

Q: 32. Differentiate the following function with respect to y. e + 3º = 1

A: This is a simple differentiation problem

Q: dy Find by implicit differentiation, given that e ! dx 9 +7 ln (x) = y. Your answer could involve…

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Q: Consider the following. Vi+ vT = 5 (a) Find y' by implicit differentiation. y' = (b) Solve the…

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Q: Consider the following equation. 6x? – y? = 5 - (a) Find y' by implicit differentiation. y' = (b)…

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Q: 10. у %3D (е 3х+4 +2)/(е2+3х +1) (e-3x -Зx+4

A: Given that, y=e-3x+1+2e2+3x+1

Q: : Answer the following two sections (A and B) (A) Find the first derivative of the following…

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Q: A function f(x) is defined by f(x) ce Find the value of the constant e for (x) dx=1.

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Q: Find the indicated derivative. for p = da 1-9 dp dq

A: We find the derivative dpdq of the given function p by using quotient rule and chain rule of…

Q: What is the first derivative with respect to x of the function g(x)= 4/9 * О 4/9 O 4 O 12

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Q: tan(x)e" x2 +1 D(r) =

A: Given function is Differentiating with respect to x by using quotient rule of differentiation which…

Q: Find the first derivative f' and the original function f. ƒ"(x) = cos(x), s' () = 5. ()=4 f' (Use…

A: Topic- differential equations

Q: Consider the following. 6 1 (a) Find y' by implicit differentiation. y' = (b) Solve the equation…

A: Implicit differentiate: - The procedure for determining the derivative of a dependent variable in an…

Q: Find the value of the derivative for the given function. dr 1 if r = de e = 2 dr (Type an integer or…

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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: