Product Rule for the second derivative Assuming the firstand second derivatives of f and g exist at x, find a formula ford2/dx 2 (f(x)g(x)).

Q: Using logarithmic differentiation find the gradient of the tangent to the curve represented by the…

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Q: Derivatives involving sec x and csc x Find the derivative ofy = sec x csc x.

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Q: 1- sin x Find the derivative of y = 1+ sin x

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Q: Finding Slope of Function When Computing Derivative Involves the Product Rule Determine the slope of…

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Q: A derivative formulaa. Use the definition of the derivative to determined/dx(ax2 + bx + c), where a,…

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Q: Second-order derivatives Find the second derivative of y = csc x.

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Q: Tangent line of a graph of f(x)=x(b^x)at x=1 is equal to the tangent line for the graph of…

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Q: First Derivative:  w=sec2x+tan2v

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Q: 15) Hyperbolic sine (sinh) is defined by sinh x = e* - e* Use this to find the derivative of…

A: Given that sinh x=ex-e-x2. Obtain the derivative as follows.

Q: Derivative of T Determine the derivative of 1. y = 100 cos 3x 2. y = 5 tan (6x - 1) 3. y = 12 cot…

A: "Kindly ask other parts in different question as per Bartleby rules." 1., 2. and 3. are solved here.…

Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable.

A: The first derivative of a function is equated to 0 to determine the points where the slope of the…

Q: Consider the function on the interval (0, 2π). (a) Find the open intervals on which the function is…

A: Consider the given function fx=x-2sin x   Find the first derivative of the function. f'x=1-2cos x…

Q: derivative of a(x) a(x)=sinx

A: Given query is to find 53 derivative of sin x.

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

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Q: Verifying derivative formulas Verify the following derivativeformulas using the Quotient Rule.

A: Given that : ddx ( cot x ) = - cosec2 x .

Q: Using chain rule evaluate the first derivative of y=x²(x+1)³.

A: We have to find first derivative of the function using chain rule: y=x2x+13 We know the formula of…

Q: Find the derivative of the function using the definitionof derivative. State the domain of the…

A: Compute the derivative of fx

Q: Derivative of the function is given. Identify critical values f'(x) = 5x(x-2)(x-5)^2/27

A: The given derivative of the function is given by:

Q: a) Using the method of first principle find the derivative of the function 1 f(x) = Show that sin* x…

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Q: State the first-derivative rule. The second-derivative rule.

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Q: Evaluate the 2nd derivative at the given point

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

Q: nction f(x) whose second derivative is f''(x) = 7x + 3 sin(x) )) = 3 and f'(0) = 2.

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Q: dx (Cosx) = -sin(x) Example 39: Use delta method to find the derivative of tanx with respect to x.

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Q: Calculate the derivative of y with respect to x. Express derivative in terms of x and y. e3xy = sin…

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Q: First and second derivatives Find ƒ′(x) and ƒ″(x).

A: Given, To find f'(x)=? f''(x)=?

Q: Compute the derivative. y = cos (te-61) (Express numbers in exact form. Use symbolic notation and…

A: y = cos(te-6t) here we use chain rule and derivate the equation  with respect to t

Q: derivative of f(x)=\sqrt(x)(1-x-x^(2))

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 4-X

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Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

A: Given: f(x)=tan x. cot x To determine: The slope of the graph of the function at the given point.

Q: sin (x) Find the derivative of h(x) %3D 2x + 5 h (x) =

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Q: find the derivative of sin(x)/2+cos(x) express numbers in exact form. Use symbolic notation and…

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Q: Find the derivative of the function y 6 tan-' (). %3D (Use symbolic notation and fractions where…

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Q: e Second Derivative Test to find all relative extrema of g(x) = x³ – 3x² +3. Show your work.

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Q: TC Find the SECOND derivative of the function f(x)=ln(tanx+secx) at x=- 3 Give EXACT value, No…

A: we are given the function,f(x)=In (tan x+sec x)

Q: sin (x) Find the derivative of h(x) = 4x + 3 W'(x) = %3D

A: Given: hx=sin3x4x+3 Use the quotient rule to differentiate the given function: ddxuv=vdudx-udvdxv2…

Q: Quotient Rule for the second derivative Assuming the firstand second derivatives of f and g exist at…

A: To Determine: find a formula for d2dx2f(x)g(x) Given: the first and second derivatives of f and g…

Q: Derivative of arctan(ln(n))

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Q: Find the derivative of the function. f'(x) = Find f'(x) when x = 2. f'(2) = Give the slope of the…

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Q: Product Rule for the second derivative Assuming the firstand second derivatives of ƒ and g exist at…

A: It is given that second derivative of f and g exist at x. Formula for d2dx2fx·gx First derivative of…

Q: using first principle Find the derivative of 1. f(x) = cosh(Inx) 2. e^sin(2x)

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Q: First and second derivatives Find ƒ′(x) and ƒ″(x).

A: Given, fx=x2-7xx+1

Q: F(x) = 4-tan(x) / 1-x^2 find the derivative

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Q: QI. Find the derivative of f(x)= 2x² - - by using the definition of derivative.

A: We have to find derivative

Q: Differentiate the function. Then find an equation of the tangent line at the indicated point on the…

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Q: Verify the derivative of cotangent and cosecant (use quotient rule). (cot(x)]=- csc (x) dx d dx…

A: Consider the formula for the quotient rule and use it for differentiation for cotangent x.

Q: Finding a Derivative of the function. 23. f(x) = sinh 3x

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Q: A. Using chain rule find the derivative of the following functions. 1) f(x) = (x³ + 3x²) 200 2) f(x)…

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Q: Calculate the derivative. y = tan -T y = 2+x 2 - x (Express numbers in exact form. Use symbolic…

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Q: Equal derivatives Verify that the functions f(x) = sin2 x and g(x) = -cos2 x have the same…

A: Given functions:                                      f(x)=sin2x And,…

Q: „sin(x) Find the derivative of : y =x) ?

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