Find a linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate. f(x) = 2 e ¯×, a = 0.11 Set the center of the linearization as x =

Q: * Part 4: A derivative computation using the FTC and the chain rule d d (F(x*) dx dt dx

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Q: Find the derivative of t(z)= (Z-2)5

A: fz=z-25z2+iz+12 Now find the derivative of fz f'z=ddzz-25z2+iz+12…

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A: Given : f(x)=(3x+1)ln(4x+3)

Q: Find the differential of the function. Y = e2x

A: Given function is  y= e2x

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A: We have to find the derivative.

Q: 2. Find the derivative of the following functions. (a). g(x) = cos (2x + 1) (b)," f(x) = In (x² – 4)…

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Q: Compute the following derivatives using the chain rule. g(y) = ln(1 + y).

A: Take 1+y = t  And use chain rule

Q: F(2) = [*e*ax e' dt

A: We have to find derivative

Q: 1. Find the derivative of f(x)= x(a+1), given a is a constant.

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Q: Find the derivative of the function

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Q: Find the derivative of the given function. y = In (- 25x² + 3x) y' =D %3D (Турe an exact answer.)

A: Solving by derivative rule

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 11) y = In 1-x (x +4)3

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Q: Find the derivatives of the functions in Exercise

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Q: Assume mmh (x) = f(g(x)) such that the first an exist g Second derivatives of both of and What is b"…

A: Assume h(x) = f(g(x)) such that the first and second derivatives of both f and g exist  We have to…

Q: Find the differential of the function. z = 3t - = zp

A: Differentiate the function: - Differentiation is that the quantitative relation of a small amendment…

Q: Find the derivative of the function at Po in the direction of A. 1- f(x, y) = 2xy - 3y² , Po ( 5,5),…

A: As per our guideline we are supposed to answer only one question you can repost other in next…

Q: Find the derivative of the function y = In(8 – e-a f'(x) =

A: We have to find derivative

Q: Find the derivative of the functions. a. y= e5x а. b. y= er-3 c. y= ecos x

A: NOTE : as per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost…

Q: Consider the derivative function h (x) = 5x³ + 3x² – 4x + 4. What is the general antiderivative of…

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Q: Find the first and second derivatives of the functions w = ez(z - 1)(z2 + 1)

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Q: let f(x,y)= z-sin(xy),x= t, y= lnt, z=e^t-1. find derivative of f directly and by using chain rule…

A: Plug the given expressions of x,y, and z. Then differentiate directly. And plug t=1

Q: Find the linearization of the function f(x) = sin(x) at a = π and use it to approximate the number…

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Q: Let f (x) = e10x. %3D Find a formula for the n-th derivative of f, for n 2 1.

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Q: The derivative of In x is and the derivative of a constant C is, sO X dx = In |x| +C for x> 0.

A: Given x>0, The differentation of natural log x is 1/x  And differentation of constant are zero.

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 1-x y = In (x + 2)5 4x - 7 (x +…

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Q: Shows the derivative function of: u³ + 2u, where u = x² + 3

A: Let's find.

Q: Find the linearization of the function f(x)=ln(2x+3) at x=-1

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Q: Obtain the derivative of the function y y = (e*1) (In(2cos(x² – 4x))

A: The given function is: y=e3x+1ln2cosx2-4x

Q: 9. Find the derivative of the function using chain rule. f(t) = 3t In t

A: To find the derivative of the function

Q: Find the differential d3y of the function y=x2ex.

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Q: Find the derivative of y with respect to t. y = t(In 1t)2

A: The given function,  y=t ln 1t2

Q: Find the differential of the given function y = xcosx

A: To differentiate

Q: Solve for the derivative of the given functions using the Chain Rule formula. Let f(x) = √(x2 + 3x +…

A: (a) fx=x2+3x+1 Inner function : u=x2+3x+1. Outer function : y=u.

Q: Find the derivative of the function f(x) = Jet – In(/x) (e+12 – 1) O (e:/2 – 1/x)

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Q: Evaluate the derivative of e22.1.png acos(b/x) COS f(x) = x2 if a = 71 and b = 0.5 at x = 2 using…

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Q: Find the linearization of the function at a. 1. f(x) = x^4 + 3x^2, a = -1 2. f(x) = sin x, a =…

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 17) y =x*in x -x3 A) 4x3 - x2…

A: Given, Find derivative of y=x4lnx-13x3 with respect to x

Q: Can you help me step by step?

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Q: Find Zxx=Zyy=Zxy=

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Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz,at the point in the direction of A =…

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Q: Find the first derivative of g(x) if g(x) = e²* In(2x) %3D

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Q: 6. у3 In (x*+3х -1)2 V(5x+2) step1 step2

A: Derivative of function

Q: Find the derivative of g(x) = J2x u²+1

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Q: Compute the derivative of x(x + 2) (2x + 1)(3x + 2) y = (a) directly using the Chain and Product…

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Q: Find the derivative of the function.

A: Given- gx=∫1cosx1-t23dt To find- The derivative of the above function. Concept Used- Using the…

Q: Find the derivative of the function: y = In e+2*+1 Oy = x"[(2x(ln x + 1) + 1] y = x*(2 + x + x² In…

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Q: Calculate the derivative of y = /x+ If the Chain Rule only needs to be used once, which functions…

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Q: 2. Find the derivative of h with respect to u if h = n²u

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Q: Find the function with derivative f'(x) = e7¤ that passes through the point P = (0, 6/7).

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Q: e2x %3D e2a + 1

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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: