Find a linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate.   f(x)= e-x, a=0.11

Q: Find the first and second derivatives of the functions in Exercises ( E q² +3 12q

A: We know that; The Power law: ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g' The Quotient rule:…

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…

Q: Find derivatives of the following functions: y= (4x + 3)/In[2x* +3x -s] y= 3(e" +e*Xx² - 4)

A: ANSWER :

Q: Find the derivative of the function. 2 a) f(x) = x² ln(x) b) g(x) = 2" + log, (x + 5) +ez c) y =…

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)…

A: To find the derivative of the functions

Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

A: x=0 is near a=0.11

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

A: We have to find derivative

Q: compute the derivative. c(t) = 1-li – e2'k - e2

A: Given  ct=1ti^-e2tk^

Q: Find the derivative of the following. g(x) (e2t + VE - t) dt g'(x)

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Q: .) What is the inner and the outer functions? b.) What is the derivative o

A: Given : The function is f(x) = x2+ 3x +1 .

Q: Find the derivative of the function. y = In(e7x + 5)

A: Given y=ln(e7x+5)

Q: Find Find the second derivative of the given function. y = In(x² – 1)

A:

Q: Find the derivatives of the functions in Exercise

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Q: Consider a function y =f(t) with domain (0. 1, 4. 2). Use the graph of the derivative function,…

A:

Q: doy= Ax²+ B Find the differential of the curve family.

A: Given curve is                                                    lny=Ax2+B we have to find the…

Q: Find the linearizationsof the following functions at x = 0. ex

A: fx=ex at x=0. Now differentiating with respect to x, we get f/x=dexdx=ex Now, f0=e0=1 & f/0=e0=1

Q: 5. Use the chain rule to find the derivatives of (a) y = log; V4 + 1 (b) y = (x – e-")²

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Q: Find the finite derivative of a the functions below at x=1: a) f(x) = 4x³-3x²+2x-3 3 b) f(x)==-²/ 3…

A: Concept: The derivative can be represented as f'(x) or ddx(f(x)) Derivative of xn: ddx(xn)=nxn-1…

Q: (b) Calculate the derivatives of the following functions. (i) y = e5x (ii) y = etan 3x (iii) y =…

A: derivative

Q: v = ) V In(2x-3y

A:

Q: 4. Find the equation of the tangent line and the normal line to the graph of the given function at…

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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: 3. Find the derivative of y with respect to x in the following functions : 18x'y (ans.: (3x-2) a)…

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Q: Find the function with derivative f'(x) = e8 that passes through the point P= (0,7/8).

A: We are given a diierentrial equatrion[f'(x)=e8x ] and a pssing point (0, 7/8) of the same  we need…

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: Q2:A/ Consider the function f(x) = 11x+3 -what are the first and second derivatives? -what are the…

A: We will answer the first three subparts of the first question as per our guideline. Please resubmit…

Q: 1 Let f(x)= J. dt. Find the derivative f(x). -dt. t4 +5 e2x none of the choices

A: Use the concept of derivative of an antiderivative and simplify.

Q: (A) Find derivative of y = In V4+ a2

A: Given that a function y (x) and we find derivative of this. We know that : d(lnx)/dx = 1/x . Here i…

Q: 1 dt t3 + 1 B Use Part 1 of the Fundamental Theorem of Calculus to find 7. g(x) = derivative of the…

A: Follow next step

Q: Find the linearizationsof the following functions at x = 0. ln (1 + x)

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Q: find a linearization at a suitably chosen integer neara at which the given function and its…

A: find a linearization at a suitably chosen integer near a.

Q: Find the first derivative of y with respect to x (y') of the given function. y = ((U^2 - 1) / (U^2…

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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: Find the derivative of the function y = 0.5 In (e +1).

A: See answer below.

Q: Q3: find the derivative of In(x4+3x-1) a) f(x) = %3D x²+1 b) f(x) = 4x³ . log(x² + 2x) %3D c) f(x) =…

A: Use product rule of differentiation.

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

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

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Q: Find the derivative of f(x)=

A: We use the quotient rule of logarithm to simplify the expression

Q: Find the derivative of the given function e5x (2x+1)5 b. f(x) = In Vx²+1 f(x) = (x In x – x)

A: Given that: b. f(x)=lne5x(2x+1)5x2+1c. f(x)=(xlnx-x)

Q: Find the derivative of the following functions: (a) f(x) = (2x – 8)(x³ + x² + 7x)| (b) ƒ(x)= x3–2x)…

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Q: a) Find the derivative of the function: T+ V3x f (x): 3x-1

A: Since you have asked multiple questions in single request so we  will be answering only first…

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 a linearization at a suitably chosen integer neara at which the given function and its…

A: The given function is fx=1+x. The derivative of the function is, f'x=1. At point a = 8.1,…

Q: Find the derivative of the given function. e5x (2x+1)5 f(x) = In Vx2+1

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Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

A:

Q: 2. Consider the function f(x) = e¯*. -2x (a) Show that the derivative is f'(x) = %3D

A:

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: