Use the derivative f' to determine the local minima and maxima of f and the intervals of increase and decrease. Sketch a possible graph of f (f is not unique). 4x 4x f'(x) = 24 sin 3x on 3'3 The local minimum/minima is/are at x=. (Use a comma to separate answers as needed. Type an exact answer, using t as needed.) The local maximum/maxima is/are at x = (Use a comma to separate answers as needed. Type an exact answer, using t as needed.) Find the intervals of increase and decrease of f. Choose the correct answer below. 27 f is decreasing on and 2n f is increasing on 30 and 2n f is increasing on and 3 3 T 2n f is decreasing on 3.0 and

Q: Use implicit differentiation to find of the following curve at the point (7, 2x). y? = x? + sin xy…

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Q: Find the Equation of tangent line of the function f(x) = 1 + csc(x) – /cos(x) 2n 4+V3 23 At the…

A: Consider the provided function, fx=1+cscx-cosx and the given point 2π3,4+323. Find the equation of…

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Q: find the derivative using the appropriate rule or combination of rules. y = (cos3 x + 3 cos x + 7)9

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Q: Find the x values of all the horizontal tangents to the function f(x) = cos.x + /3 sinx on the…

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A: Consider the following equation:

Q: Use the First Derivative Test to find the relative extrema of ƒ(x)=· sin x on (0,27).

A: The given function is- fx=x2-sinx  Differentiating f(x) w.r.t x- f'x=12-cosx Put f'x=0,…

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A: Given Trigonometric Expression: sin-11-t We can differentiate this trigonometric function with the…

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A: Given function is y=arctan1-x1+x We know that ddxarctanx=11+x2 Therefore, dydx=11+1-x1+x2ddx1-x1+x

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Q: Determine the derivative of the function defined by h(x,y) = Arctan (2) + V3Arcsin () at the point…

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Q: Use the first derivative test to find and classify the relative extrema of x2 +8x+ 16 f(1) = For…

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Q: find the derivative of y with respect to the appropriatevariable. y = (sech θ)(1 - ln sechθ)

A: We have to take derivative with respect to θ. dydθ=sinh θ ddθ1-ln sech θ+1-ln sech θddθsinh θ

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Q: find the derivative of y with respect to the appropriatevariable. y = cos-1 (1/x)

A: To find dydx, rewrite the equation and then differentiate with respect to x.…

Q: Find the derivative and simply. (a) f(x) = 1+cosx 1-cosx

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

Q: The implicit curve given by the equation x + xy + y= 1 has derivative dy 2x+ y %3D dx x + 2y Show…

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Q: Use the first derivative test to find the local extrema of the following function: f(x) = sin x –…

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Q: Find tangent line for the following f(x) = ( 4x² – 3)² f(x) = sin(8 x) at (7, 0) and (T, 1). 9. at…

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Q: fcx)= Y文 メ ー^

A: Local extrema

Q: find the derivative of y with respect to the appropriatevariable. y = ln (tan-1 x)

A: The given function is y=lntan-1x

Q: Find the derivative of y with respect to the appropiate variable show all work Y= tan^-1 (ln x)

A: Given function is y=tan-1lnx. Given function can be written as tany=lnx. Differentiating the above…

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A: 1. y=2x+7-x3+3x-12. fx=1x at the point x=2

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A: Answer

Q: Find the derivative of y with respect to x. 1/9x²-1 + sec -13x, x> y= cot %3D

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Q: ■ Find the derivative of the function. Simplify wherepossible.  y = arccos (( b+a cos x)/( a+ bcos…

A: Quotient rule of differentiation:       Chain rule of differentiation:…

Q: Find the derivative for x+1 a)f(x)=- x-4 b)f(x)= sin' 2x Show the work on your notebook, take a…

A: (a) To find: The derivative of fx=x+1x2-4. Formula used: Quotient rule of derivative:…

Q: Find the tangent line approximation for f(x) = v2 – x at x = -2. Use it to estimate the value at x =…

A: Solving using linear approximation formula

Q: 2. Find the derivative of y = tan°(/1 – x²). Make any obvious simplifications. %3D

A: Using chain rule of differentiation.

Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – /cos(x) (2n 4+V3 2V3 At the…

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Q: f(x) = sin° (tan(5e2*))

A: We can find the derivative as below using chain rule.

Q: Find the x-value of the extrema by using the Second Derivative Test. Justify your answer. f(x) =…

A: As per the question, we need to find out the x value of the extreme, for bubble 3 only. For (3),…

Q: If f(x) = = f'(x) = 3x (sin x + cos x), find f'(x). Evaluate the derivative at x = 4. Enter an…

A: Given: fx=3xsinx+cosx To find : f'x and to evaluate the derivative at x=4. To evaluate the…

Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – /cos(x) (2n 4+v3 3' 2v3 At the…

A: Given: f(x) = 1 + csc(x) -cos(x)   To determine: Equation  of the tangent line at the point…

Q: find the derivative of y with respect to the appropriatevariable. y = sin-1√2 t

A: To find the derivative of y=sin-12t

Q: Find all points with x-values on (0, 2π), where tangent line to the graph of f(x) is horizontal.…

A: Find all points with x-values on (0, 2π), where tangent line to the graph of f(x) is horizontal.…

Q: Identify the most appropriate differentiation rules to be used in finding the derivative of the…

A: Given :1) y=(2x+7)-(x2+3x-1)find tangent :2)f(x)=1x at x=23) f(x)=x-2x+3 at x=2

Q: find the derivative of y with respect to the appropriatevariable. y = sinh-1 (tan x)

A: The given function is: y = sinh-1 (tan x) The derivative of y=sinh-1θ is: ddθsinh-1θ=11+θ2.

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

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Q: y = cos t

A: We have y= cos t By using limit definition of derivative

Q: Find all x values on the graph of f(x) = - 3 sin x cos x where the tangent line is horizontal.

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Q: find the derivative of y with respect to the appropriatevariable. y = 1/2 sinh (2x + 1)

A: We have to find derivative of y with respect to the appropriate variable: y=12 sinh 2x+1 We know…

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Q: Find the derivative using the appropriate rule or combination of rules. y = (cos 6x + sin x2)1/2

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Q: Find all points on the graph of the function f(x) =2 Sin x + Sin2 xat which the tangent line…

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Q: If f(x)=4x(sinx+cosx), find f'(x) f'(x)= Evaluate the derivative at x=2. Enter an approximation,…

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