Use the sign of the derivative to establish the inequaltiy ln(1 + x) > x − x2 2 , ∀x >0

Q: Find the equation of the tangent line to the function f(x)=−3x2−2x at the point where x=1. Give your…

A: Here we find the equation of tangent line of the function fx=-3x2-2xat x =1

Q: Find the first derivative of g(x) = 2 ln(x)tan(x*). 2 tan(4) g'(z) = | 82 sec²(4) In(z)+ X syntax…

A: We will solve the problem. The syntax error is ln(x4)  instead of 'CAPITAL i'. Refer to the final…

Q: Find the derivative of the function by the limit process. Find an equation of the tangent line to…

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Q: Use the Power Rule to compute the derivative. (Use symbolic notation and fractions where needed.) L-…

A: ddttn=n.tn-1

Q: find the tangent line of f(x)= 3x-4/x+1 at x=0

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Q: Find an equation of the tangent line to the graph of y = f ( x ) at the point on the graph where x…

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Q: 8 Find the derivative of: 2/x + x3 Type your answer without fractional or negative exponents. Use…

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Q: Use logarithmic differentiation to find the derivative of the function. y = (sin(7x))ln(x) y' =

A: We have to find derivative

Q: 10) Using the First Derivative Test, what are the local extrema for the function 5(x)==x²+10 x³…

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Q: Use logarithmic differentiation to find the first derivative. Enter your answer without fractional…

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Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

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Q: Show that (x ln(x)) ‘ = 1 + ln(x) using the Product Rule for Differentiation.

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Q: a) Find the derivative of the function using limits: f (x) = 2x+1 b) Find an equation of the tangent…

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Q: find the second derivative and simplify the final result 9. xArctanx - ln (square root of x^2 + 1)…

A: y=x tan-1x-lnx2+1

Q: Use logarithmic differentiation to find the first derivative. Enter your answer without fractional…

A: Given:     To determine:

Q: 2. Identify the derivative (9) based on the product rule ie, (G). Simplify to a single term.

A: Given ∂∂TGT

Q: f(x)=−2x3+x2. Determine the equation of the tangent line at x=1.

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Q: Use the definition of derivative (do NOT use the short cut method) to find f'(x) given that f(x) =…

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

Q: sin(x') In(5x + 7x- 3) 6) Find the derivative of: y =

A: Formula 1: Let f(x) and g(x) be two functions, then f(x)g(x)=g(x)f'(x)-f(x)g'(x)(g(x))2 The given…

Q: Find derivative of f(x) = ln(5x + 2) The slope (as fraction) of the tangent line at x=2 is

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Q: Use logarithmic differentiation to find the derivative of y=(2x)2x

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Q: 3) Find the second derivative of 2x f(x) = for x + 0 3x2+4x Show all steps. Simplify your answer as…

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Q: Find the derivative of f(x) = = 4√√x + 2 x7 . Type your answer without fractional or negative…

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Q: Find the derivative of f with respect to x of f(x)=ln x8.

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Q: A box with a square base and open top must have a volume of 78732 cm, We wish to find the dimensions…

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Q: Find the equation of the tangent line to the function f(x) = ln (7 – 4x) at x = 1. (Use symbolic…

A: Slope of the tangent is obtained by dy/dx

Q: What is the anti-differentiation rule to be used in order to integrate the function f Vx5 dx. a.…

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Q: Find the derivative. f(x) = 2^x {ln[cot(x)]}^2

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Q: Use logarithmic differentiation to find the derivative of the function. y = (ln(x))cos(5x) y' =

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Q: Find the equation of the tangent line to the function f(x) = ln (22 – 7x) at x = 1. (Use symbolic…

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Q: wwww To find the slope of the tangent line to y = ln(x²) at the point (1,0) we must find the…

A: Recall: Slope of the tangent line

Q: Using method of sub., find the Anti-derivative 1 x In x

A: detailed solution is given below

Q: Find the derivative of y = cosh(11x) for x > . (Use symbolic notation and fractions where needed.)…

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Q: Find the equation of the tangent line

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Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

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Q: 4 Find the derivative of: – 9/x - Type your answer without fractional or negative exponents. Use…

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Q: Find the derivative using logarithmic differentiation. x(x + 4) (5x + 1)(3x +7) (Express numbers in…

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Q: Find the derivative of the following function using the LONG METHOD (limits). Provide your…

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Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

A: Applying natural logarithm on both sides, we get

Q: Using the First Derivative Test, what are the local extrema for the function h(x) = 3x3 – 9x2 – 72x…

A: It is given that,              h(x)=3x3-9x2-72x+9we have to find the local extrema of the function.

Q: Find the equation of the tangent line to the function f(x) = ln (13 – 4x) at x = 1. (Use symbolic…

A: We have to find the equation of tangent of ffx=ln13-4x at x= 1 at point x = 1

Q: Find the derivative of y sinh-(13x). (Use symbolic notation and fractions where needed.)

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Q: Find an equation of the tangent line to the graph of y = f ( x ) at the point on the graph where x…

A: The slope of the tangent line of a graph y = f(x) at a point x0 is given by the derivative of…

Q: 5. Find the second derivative of f(x) = arctan(2x"). (You do not need to simplify your answer.)

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Q: Use central-difference method to approximate the derivative of f(x) = In x² with value of x at 1.8,…

A: In this question we are given that f(x) =ln (x2) We have to find the value of f'(1.8) with the ∆x =…

Q: 27. Find the derivative of f(x) = (1 + 2x²)(x – x²) in two ways: by using the Product Rule and by…

A: Derivative of the function f(x) is given by

Q: Determine the equation of the tangent line to •x³ +ln x the graph of f(x) at x = 1. [² = √/3 + 5t5dt

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Q: find the equation of the tangent line to the graph of the function y = ln(x^2) at the point (3, 1).

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Q: what’s the derivative ? f(x)= ln(x^3 - 7x^2 + 1)

A: topic - derivative of a function

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: