tion of the tangent line to f(x) = 4 %3D

Q: Anti-derivative of this function:  h(θ) = 4 csc θ cot θ + 2 sec2 θ

A: Indefinite Integration

Q: 11. y=3x+ ln x %3D

A: Topic - derivatives

Q: 2. Find the derivative of y = 2 1 1- x² + arcsin x 2

A: As per our guidelines, I can answer only one question and maximum three subparts of a question.…

Q: Find the nth-order derivative of the function y=arctanx at the point x=0.

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Q: 1. у %3D х+/x

A: Topic = Derivative As per guidelines , At  a time only one question can be answered out of different…

Q: Find the derivative of the function. 1 + x 1 - x y = arctan y' =

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Q: What is the average rate of change of the function f(x): = x² between x = -3 and x = 3?

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

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Q: Find the equation of the line tangent to the graph of y = 4 ln(x) at a = 2. Enter exact values.…

A: detailed solution is given below

Q: The slope of the tangent line to the graph of the function at the point. V The average rate of…

A: We have to check

Q: 5. Second derivative of y = 1+t)< t2

A: Given: y = 1+t2t2 To find: Second derivative of the given function.

Q: Where is the function defined by ƒ(x) = ex increasing?Decreasing? Where is the tangent line…

A: Where is the function defined by ƒ(x) = ex increasing? Decreasing? Where is the tangent line…

Q: A farmer wants to fence in 800 ?t2 of land in rectangular plot to be used for different types of…

A:

Q: 5th derivative of y = log x^5 to the base 2

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Q: Find the derivative of the function: f(x) = ln X x+1* Is there a shortest way? Please explain.

A: We can find the answer in the following steps.

Q: calculate the derivative. y = sinh x tanh x

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Q: 23. The slope of the tangent line indicates the rate of change of the function, also called the 24.…

A: Since, you have asked multiple question, we will solved the first question for you. If you want any…

Q: .Find the derivative of the function y = cosh*x- sinh“ x

A: As per guidelines we can solve only one question at a time, if you need more answer kindly repost…

Q: y = Vx * sin3x

A:

Q: Determine the first derivative of the ff. function y = 2 + arctan(3 sec 2x)

A: We have to find the first derivative of the function: y=2+tan-13 sec 2x We know the formula of…

Q: Estimate the instantaneous rate of change at the point x=2 for f(x)=ln(x) ROC =

A: the fiven function is f(x)=ln(x)

Q: 4. Find an equation of the tangent line to the graph of f(x) = ln(x ^2 + 4) at the point (2, ln(8))

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Q: 3 + 2x +5

A: GIVENy=x3+2x+5   and x=2

Q: 3e* at the point Estimate the slope of the tangent line of the function f(x) x=e (Use decimal…

A: Firstly, we find derivative of f(x) by using the result that derivative of e^x with respect to x  is…

Q: calculate the derivative. y = ln(coth x)

A: Given: y = ln cot hx To find: The derivative of the function.

Q: (1 point) Find dy/dx by implicit differentiation. x + y = 6 + x

A: Given: x+y=6+x2y2

Q: 1) Find the derivative of the function 2 + X y = arctan V 2 – x .Simplify where possible.

A: Answer and explanation is given below..

Q: Find the derivative of the function. y = 3 x tanh-1 x + 3 In/1 - x2 y' =

A: Product Rule of Differentiation : d(u.v)dx = u.dvdx+dudx.v

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: Find the slope of the tangent line to the exponential function at the point  (0, 1). y = ex/3

A: Slope of tangent line is derivative of the given function at that point.

Q: Find derivative of f ( x ) = x^3 e^x The slope (rounded to whole number) of the tangent line at x=2…

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Q: State the derivative rule for the exponential function ƒ(x) = bx.How does it differ from the…

A: Derivative rule for bx. The derivative of fx=bx is given by f'x=bx lnb.

Q: 2 Find the derivative of y = arctan(x´ + 3)

A: We have to find the derivative of the given function.

Q: Determine the x-values where relative extrema occur for y = (x² +x – 12). Use the second- derivative…

A: Here y=x2+x-122 ⇒y'=ddxx2+x-122       =2x2+x-12ddxx2+x-12       =2x2+x-12(2x+1) for critical points,…

Q: Molar volume is a function of temperature and the pressure or V = f (T, P) ; and its total…

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Q: Find the equation of the line tangent to the graph of y = 6 ln(x) at x = 3. Tangent Line: y =

A: We have to find the slope of tangent at first.

Q: Find the derivative of the function y = x tanh−1 x + ln√(1 − x2)

A:

Q: Find the equation of the line tangent to the graph of y=(x^2−x)ln(7x) at x=2. Round to three…

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Q: water leaking onto a floor creates a circular pool with an area that increases at the rate of 3…

A: Let  A=π r2 differentiating A with respect to time tdAdt=2πr…

Q: Find the equation of the tangent line to the curve y = ln(4 ln x) at the point where x = e. %3D

A: It can be solved using differentiation.

Q: Find teh average rate f change of f(x)=3x^(2)-x from x_(1)=-1 to x_(2)=2

A: Solution: The objective is to find the average rate of change of the given function

Q: Estimate the slope of the tangent line of the function f(x) = 7e* at the point x = e. (Use decimal…

A: We find f'(x)

Q: nd derivative of f(x) = x In(x)

A: We have to find the second derivative of the given function

Q: The tangent line to the graph of y=f(x) at the point (7,55) has the equation y=8x−1 (a) Find f′(7)…

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Q: Find the derivative. y(x) = x tanh−1(x) + ln (sqrt (1-x^2))

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Q: Graphically, the instantaneous rate of change of a function at a specific x-value can be estimated…

A: Given: The below four statements are given: (a)Determining the slope of a single secant line on the…

Q: Find the derivative. f(x) = x sinh(x) - 4 cosh(x) f'(x) =

A: Given problem is :

Q: What is the difference between a derivative and an integration?

A: We have to state the difference between a derivative and integral.

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

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: