Differentiate the function. f(x)  = In 1/x

Q: Differentiate the following function.   y =ln (x2 + 1) / (2x + 3)

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Q: Differentiate the following function.   y =  ln -2x + 1

A: Given function is y=ln-2x+1. To differentiate the given function. Solution: Chain rule of…

Q: Differentiate and simplify this function g (y) = y3 / ln(2y)

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Q: The fifth derivative of the function f(x) = 5x° is a constar False O True

A: Given query is to find statement is true or false.

Q: Describe the domain of the function f(x, y) = ln(7−x−y).

A: (18)

Q: All boxes with a square base, an open'top, and a volume of 160 ft have a surfac the surface area…

A: The surface area of the box S(x)=x2+640x ...............(1) differentiate with respect to x,…

Q: Find the average rate of change of the function from x1 to x2. f(x) = √x from x1 = 9 to x2 = 16

A: Now,

Q: Find the average rate of change of the function from x1 to x2 : f(x) = √x from x1 = 4 to x2 = 9

A: Given fx=x and x1=4 , x2=9Average rate of change ,△fx△x=fx2-fx1x2-x1

Q: 2 Using the definition of derivative, prove the following: (a) f'(x) = x if f(x) = x %3D

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Q: Approximate the function at the value of x to four decimal places.

A: f(2)=ln 2+1+e2=ln (3)+e2

Q: h) f(x) = e4sin(5z+2)

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Q: Find an expression for the derivative of h(x)=ln(f(x)). answer in terms of f and f'.

A: The given function is  h(x) = ln(f(x))

Q: 12. h(x) = ln (x + vx² – 1

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Q: Consider the function f(x) = (x² – 6)(a² – 6æ) Compute the derivative. f'(x) =

A: In this we are going to use product rule of derivative to find out the solution so I'm providing…

Q: Consider the function f (x) = x³ + 3x + 2. Calculate the average rate of change from x = 1 to x = 3…

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Q: Find the derivative of f(x) = x"'log,(r + 3). f()=

A: The given function is: f(x)=x8log2(x+3)       =x8ln (x+3)ln 2(used change of base in logerithm)…

Q: Find the domain of the function g(x) = /1 – x ln x

A: We have to find domain

Q: Find the average rate of change of the given function on the interval [0,3]. F(x)=-x^2+2x+2

A: Topic = Functions

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

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Q: Determine for what values of x the function f(x) = 32 ln(x) − x^2 + 6x − 5 has a tangent line with…

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Q: The Range Rf for the functionf (x) = tanhx is:

A: Range of f(x)= tanh x

Q: y = cosº (4x)

A: Given: y=cos94x As we know that: The Power Rule: ddxxn=nxn-1 The Chain Rule: fgx'=f'gx·g'x

Q: F(s) = ln In s

A: We know ddx(ln x)=1x   Chain Rule : ddxln f(x)=1f(x)·f'(x)

Q: Let f(x) = derivative f'(x) equals o. e. Find the value of x for which the second

A: Given that: f(x)=32x2-ex

Q: Find the average rate of change of the function from X1 to X2 f(x)= -3x2-x  from X1= 5 to X2= 6

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Q: +V2x y =

A: According to the chain rule of differentiation:

Q: find the extreme values on the interval f (x) = x − 12 ln x, [5, 40]

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Q: Differentiate the following functions: 1. f(x) = ecosx

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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: Find the average rate of change for the function between the given values. 3) f(x) = x2 + 7x; from 1…

A: We have to find average rate of change

Q: Find the derivative of the function. f(x) = logg(x) f'(x) =

A: Derivative Question

Q: Find all the relative and absolute extrema of the given function on the given domain f(x) = x^2 +…

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Q: Find the first derivative of the function * 4 f (x) = Væ + 4

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

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Q: Find the derivative of the function. 4 f(x) x In(x) f'(x) %D

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Q: Find f''(x) for: f(x)=ln⁡x/4x

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Q: Find the derivative of the function.

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Q: Consider the function f(x) = x3 + 5 Compute the derivative. f'(x) =

A: we have to find derivative

Q: What is the first derivative with respect to x of the function g(x) = 3/9 9. O 1/2

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Q: 5) Use the tangent line at x = 9 to approximate the value of the function f(x)= Vx at x= 8.8.

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Q: 2. Using the definition of derivative, prove the following: 1 (a) f^(x)= if f(x) = Vx %3D

A: fx=x3

Q: Consider the following function. f(x) = x3/2 Find its average rate of change over the interval [1,…

A: The objective is to find average rate of change over the interval [1, 16].

Q: 2. Use the definition of the derivative of a function at a number to calculate f'(8) where f(x) is…

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Q: 10 The derivative of the function f(x) = x7 + - 10 726 + (r³) 10 71° + (2) 1 10 7x + 10 10 726 (z²)…

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Q: 8 Find the derivative of f( x ) = x° log, (x + 3). f'(x) : = (x).f

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Q: Find the derivative of the function. f(x) = log (x) f'(x) =

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Q: find the derivative of the function  F(x)= e^x/e^x + 8

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Q: Use the second derivative to determine f"(3) for the function f(x) = x² In (x) 2ln(3) +2 O 3ln(2) +3…

A: topic - derivatives

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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Q: What numerical value for A makes the function contnuous at the seam?

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