Diffrentiation Formulas (derivative) Determine where, if anywhere, the tangent line to f(x)=8+4x+x2−2x3f(x)=8+4x+x2−2x3 is perpendicular to the line y=−14x+83y=−14x+83.

Q: 3. Approximate the first order derivative of f(x)= x² + 2x at x = 3, using Forward, Backward and…

A: Formulas for differences are enclosed next page

Q: A function f has the tangent line y=2x+1 at the point (3,7). Find the equation of tangent line of…

A: Given data:     The given expression for the function is: y=2x+1. The given point is: (x1,y1)=(7,3).…

Q: B) Derivative following functions by using chain rule method 1) y = 5u³- u? , 2x = 4u? 2) у %3D |1 ,…

A: Answer (1): Given that, y=5u3-u2, 2x=4u2 Suppose fgx Then, to find the derivative apply the chain…

Q: f(x+Ax)- f(x) Using the first principle of derivative f'(x) = %3D Ax Ax-0 Differentiate: y 4x - 6

A: Derivative of the function

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: Differentiate both sides of the equations. Use chain rule for differentiation.

Q: valuate the second derivative of the function at the given point. Use a computer algebra system to…

A: The derivative of the square root function is calculated using the formula ddxxn=n·xn-1. The value…

Q: Derivative of y = (x(1-x^2)^3)/((1+x^2)^1/2)

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Q: f(x)= (3x²+2x+1)

A: Topic = Derivative

Q: using the equation f(x)= x^2+x find slope of tangent line f′(2) using the limit definition of a…

A: The slope of the tangent is given by f'(x). We will use the limit formula to find f'(x)…

Q: Use the second derivative to discuss concavity. The second derivative is y’’ ={2x(x2+3)}/ (x2-1)3

A: given,  y''=2xx2+3x2-13 we have to discuss the concavity using second derivative.

Q: derivative of the firm's profit function is F'(x) = -0.03x2 + 3x - 100, where x > 0 is the output…

A: We will use the basic knowledge of functions and derivatives of functions to answer this question.…

Q: Find the derivative of the function using the definition of derivative. f(x) = x° - 5x + 9 f'(x) =…

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Q: Puestion 4. Using the definition of the derivative, show that f(x) = ifferentiable at x = -3. |2x+6|…

A: we have to show

Q: derivative of the firm's profit function is F'(x) = -0.03x2 + 3x - 100, where x 2 0 is the output…

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Q: Find an equation of the tangent line to the graph of the function f through the point (x0, y0) not…

A: The given function is fx=x.

Q: Find the equation of the tangent line to the curve y=8ln(x3 −63) at the point (4,0)

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

A: Here we differentiate and find the equation of tangent.

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: equation of tangent line of f(x)=5x^3+1 at x=1 is * O y=15(x-1) O y=15 x-9

A: Given: The function f(x)=5x3+1 and a point x=1

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

A: Given: The first and second derivatives of f and g exist at x

Q: True of False: Derivative of (arctan(e^(-x^2))) = [-2xe^(-x^2)] / [1 + e^(-2x^2)] Show your…

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Q: Using derivative Find the slope and the equation of the tangent line to the curve y=x²+1 at x=0.…

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Q: valuate the second derivative of the function at the given point. Use a computer algebra system to…

A: h(x)=193x+13 , at the point 1,649

Q: Find the slope of the tangent line to the graph of the function at the given point. f(x) = 9x − 2x2…

A: Given function f(x) = 9x-2x2

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: Find the equations of the two tangent lines to the graph of f that pass through the indicated point.…

A: Given function is fx=4x-x2

Q: Using Chain Rule method Find the derivative of: 5 2. F= x³ + x² + x + 1 1. F(x) = ln Cos(x²)

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Q: e product rule can be used to find the derivative of which functions. A. f(x)= (2x-3)^10 B. f(x)=…

A: Given function fx=sinxcosx Differentiate the above function w.r.t 'x' f'x=ddxsinxcosx

Q: derivative of y= (cosx)^x

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Q: = (x2 +x – 12). Use the second- 1. Determine the a-values where relative extrema occur for y…

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

A: Given,           fx=16-xTo find: The derivative of the function. and domain of the function, and…

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: (x+ Ax)-S(x) Use the definition of the derivative f'(x) = lim Ax0 to find the equation of the line…

A: Use definition of derivative

Q: f(x+Ax)-f(x) Use the definition of the derivative f'(x) = lim Ax-0 to find the equation of the line…

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Q: Derivative of ln[cosx/4-3x^2]

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Q: 7. Find all relative extrema. Use the Second Derivative Test to identify the local extrema. 2 f (x)…

A: Given:The given funtion is f(x)=3x+2xTo findWe have to find the relative extrema of the…

Q: Find the equation of the tangent line to the graph of the given function at the point with the…

A: Here we have to find the equation of the tangent line to graph of the function y =f(x)=4x2. Given x…

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

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Q: A. Find the slope of the curve y = x² - 2x - 4 at the point (2, -4) by finding the limiting value of…

A: A. Find the slope of the curve y = x² - 2x - 4 at the point (2, -4) by finding the limiting value of…

Q: derivative of  f(x) = x csc(x) - 4cos(x)

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Q: uestion-9 a) Using 2nd derivative test, find the absolute extremes of f(x) = x – Vx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: A differentiable function has the value y(2) = -1 and the derivative value y'(2) = 3. Approximate…

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Q: how do you find the  (a). equation of the scant line through the points wehre x has the given…

A: The given equation is f(x)=x^2+2x.

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

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Q: Use the fact that the derivative of the function f(x) = is f'(x) = - to find the equation of the…

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

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Q: Using differentiation rule, find the derivative of the function ƒ (²) = [2 + (² ² + 1)²³ at _z = 1 +…

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Q: Derivative of g(x)=[(ex+1)/(x+1)]2

A: Given g(x)=ex+1x+12                 =e2(x+1)x+12 We find the derivative by the following method…