Estimate v16.3 using the linearization L(x) of f(x) = /x at a = 16. (Use decimal notation. Give your answer to three decimal places.)

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: At what time does f (t) attain its largest value?

A: Consider f(t) is any function. We know that function attains its largest or smallest value when the…

Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: y=57x3+1-3

Q: Find the derivative of the composite natural exponential functions 1. f(x) = In( 2. g(x) = In(v³ +1)…

A:

Q: Find the derivative of the function

A: Given  that y = ( ax+ √(x2+y2)) -2 Method used- Chain rule- The chain rule states that the…

Q: Compute the derivative of the given function. g(t) = 2t - In(2 – 5t) %3D

A: Given that: g(t)=23t.ln(2-5t)

Q: Determine the orthogonal trajectories y-3x+1=ce 3x

A:

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

A: Given y=ln(e7x+5)

Q: Compute the derivatives at the given value of a g(x)=(3x-5)/(x-2)     a=1

A:

Q: The following linear model dx x(0) = 1000 6x, dt describes growth of populations Select one: True…

A: True.

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

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

Q: Q2/ Find the orthogonal trajectories of the family of curves x-y - c² YAS

A:

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: 11. Find the linear approximation of f(x) = √√x_ at a = 1. Use the linearization to estimate the…

A:

Q: Find the orthogonal trajectories of the following family: y = Ce-x

A: First differentiate then  solve

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

A:

Q: Exercise 10. Find the derivative d 7x (* + 2) dt dx

A:

Q: Q2/ Find the derivative of the function f(x) = V3x +1 by definition %3D

A:

Q: write the function as a composite f (g(x)) and compute the derivative using the Chain Rule. y =…

A: Given : The function is y = cos ( x3 ) .

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative.

A:

Q: Find the orthogonal trajectories of x² + y² – 2cy = 0

A:

Q: Find the derivatives of the functions in Exercise

A: Explanation: Given that,  w=(2x-7)-1(x+5)     Formula used: According to the product rule of…

Q: Find the orthogonal trajectories of the family of 1 curves Y= X + k

A:

Q: compute the derivative. g(t) = e4t−t2

A: The derivative of a function is given by the expression f'(x)=limh→0f(x+h)-f(x)h. For some standard…

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

A: The nearest integer to a=-0.9 is -1 because at this point, we can easily find the function's value…

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

A:

Q: Find the derivative of the function. y= log , (3x2 - 2x) 5/2 O A. In 9(3x- 1) (3x2 - 2х) OB. 10(3x –…

A: We need to apply 1.chain rule 2.differentiation of logarithmic   we get option c as correct answer

Q: Find the derivative of the linear fractional function y=ax+bcx+d.

A: We have to find the derivative of    y=ax+bcx+d ddxy=ddxax+bcx+dWe have to apply division rule…

Q: Find the linearization of ƒ(x) = √1 + x at x = 0

A: Consider the following function: fx=1+x Differentiate fx with respect to x: ddxfx=ddx1+xf'x=121+x

Q: 3t – 2 dt t + 1

A:

Q: g(=) = / Compute the derivative of g(x) dt. -2xe5 - 2xe - 2xe

A: Given           g(x) = ∫x21et3 dt

Q: Compute the derivative of g(æ) = e dt. 22 -2xe -2xe O -2re

A:

Q: if the implicit function is x3=at2, find the d2x/dt2

A: if the implicit function is x3=at2, find the d2x/dt2

Q: y = log4 x %3D .y = In(5x2 -4x + 8) %3D

A:

Q: Find the orthogonal trajectories of У — сх CX

A:

Q: Suppose h(x) =log,(3x+1). What is the correct result Зх + %3D of the derivative of h with respect to…

A:

Q: x² – y² = = CX

A: For orthogonal trajectories, replace dy/dx by -dx/dy and solve it.

Q: Find the differential of the function. u = 3x4 + 4

A: The given function u=3x4+4

Q: compute the derivative g(t) = e4t−t2

A:

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

A: Derivative of function

Q: Evaluate the second derivative of h z f8.png asin (bvx3) f(x) c2x + In(kx) if a = 16.55, b = 3, c =…

A: The Backward Difference Approximation(BDA) uses the formula below to approximate the double…

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: Use the u-substitution to find the anti-derivative of h'(x)= xcos(2-3x2)

A: h'(x)=xcos(2-3x2) Formula ∫cos (x) dx= sin (x)+C

Q: a derivative computation using the FTC and the chain rule t): df 13

A: Given : ddxFx3 =ddx∫13x3e-t2dt

Q: Find the linearization L(x) of y=e10xln(x) at a=1

A: y=e10xln(x)  The linearization L(x) of a function f(x) at x = a is, Now  Now differentiating given…

Q: et dt. · e2t 5. Find and simplify the derivative of f(x) = %3D 1 -2 In z

A: Assume g'(t) = e^t/(1-e^(2t))

Q: determine the equation of the orthogonal trajectories of the following families curves: e^x+e^-y=C1

A: