Let f(x)=4x^2−9x. We want to estimatef(4.05)f(4.05) using linear approximations.

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Q: By using the definition of the derivative, find the for: - dx 1- f(x) = Vx

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Q: Find the derivative of the function y = 2x sinh−1(2x) − √(1 + 4x2)

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Q: y = 2 ||

A: We have to find the derivative of the function y = 1-x2ex2

Q: Find the 3rd derivative of the function y=xsinx

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Q: (x²+1)* V1-x y = In

A: Use the chan rule of derivative then simplify the result.

Q: calculate the derivative

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Q: Calculate the derivative of the function y=1+cosxsinx.

A: Given: y=1+cosxsinx we know that for finding derivative of given function we need to use product…

Q: Find the derivative y = cosh(2x)

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Q: find the slope of tangent line to curve y^2+x^2=y^4-2x at (-2,1)

A: Given function y2+x2=y4-2x  We have to find slope of tangent line at(-2,1).

Q: What is the derivative of * y = arctan(x2 + 1)?

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Q: Find the tangent line to the curve y = x^2 −5x + 11 at the point (1, 7). Use the limit definition of…

A: slope of the tangent line is m=dydx at (1,7)   By limit definition of…

Q: Find the first derivative y= etanx

A: We have to find first derivative of    y=etanx   First derivative is dydx

Q: Use the First Derivative Test to find the relative extrema of x – 3 f(x) ex

A: The given function is fx=x-3ex. We need to find the realtive extrema. Concept used:  Consider x=c is…

Q: 1 y = ┤㈑┤慈┤

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Q: Find derivative of y=xsin2x

A: We will need product rule. Assume, u=x and v=sin2x. Now, we have u=x ⇒u'=dudx=dxdx=1  and v=sin2x…

Q: Find the derivative. y = ecosh(8x) y'(x) =

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Q: Find the derivative. y = (lnx) 2

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Q: Estimate the derivative of f(x) = sinx at x = π/6

A: Since,it is known that the derivative of the function with any variable measures the rate of change…

Q: Find the slope of the tangent line to the curve y2+x2 = y4-2x at point (-2,1)

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Q: Find the slope of the tangent and normal to the curve  y=2x2+3sinx at x=0

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Q: Find the nth order derivative of the square root y=√x.

A: Let's first calculate the nth order derivative of the power function y=xm where m is a real number.

Q: Find the equation of the tangent line to the curve y = xV13 – x² at the point (2,6).

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Q: Where on the curve y = (121+ x²) * does the tangent line have the greatest slope? NOTE: Enter the…

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Q: Find the slope of the tangent line to the curve x – 4xy + y° = - 23 at the point (- 3, – 2).

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Q: The slope of the tangent line to the curve y = 3 3 at the point (5,2) is: X -

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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: Find the equation of the line that is tangent to y = 2log3(x + 1) and is perpendicular to the line y…

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Q: A piece of wire, 370 cm long, is to be bent into an isosceles triangle. What should the exact…

A: given: A piece of wire, 370 cm long, is bent into an isosceles triangle. we have to determine what…

Q: What is the derivative of y = arctan(x² +1)?

A: Find the derivative of the function

Q: Show that the rate of increase in the slope of the tangent at a point on the curve y = 2x3 is 12…

A: Consider the given curve: Here the objective is to show that the rate of increase in the slope of…

Q: 7. y = Vx + 2

A: Using Delta method differentiate y. And using rationalising.  Follow step 2nd  .

Q: Find the derivative of y = 21+arctan x

A: By using derivative formula

Q: i.) Find the tquation of the tangent line to the curve y= 2+4x- x° at the point P(-1,-1)

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

Q: Determine the derivative -d/dv y = 2x³ + 5x - 6 y 1 x² 3x 6x³ + x² − 10x − 3 -

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Q: What is the Derivative of: y = extan x

A: Given: y=ex tan x To Find: dydx=?

Q: Find the average rate of change and the equation of the secant line for 2x f (x) = from -1 to 3. x²…

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Q: Find the slope of tangent line for the equation x^2+y^2=5 on (1,2)

A: The given equation of the line is,

Q: Find the derivative of the function. y = etan(8) y' =

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Q: calculate the derivative y = cosh−1(3x)

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Q: Find the nth order derivative of the cube root y=3√x.

A: We first find the first three derivatives using the power rule

Q: Determine the point on the curve where the slope of tangent line to the curve is 0 or -3 a) f(x)=…

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Q: Find the slope of the tangent line to the curve y=4x^3-x at x=1. What is the equation of the line…

A: Given: The equation of a curve is y=4x3-x . The slope of the tangent to the curve at the point x=1…

Q: By using the definition of the derivative, find the slope of the tangent line to the curve y = 4x −…

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Q: Locate the point where the slope of tangent line to y-n 2r2 s

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Q: Find the instantaneous rate of change cope of the tangent line to 2 (3,-2) 1

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

Q: 2 Use the definition of derivative to find the equation of line tangent to f(x) = 2 through x = 3.

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Q: y=

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Q: calculate the derivative y = (sinh−1(x2))3

A: Given The chain rule of derivative is given by: The derivative of the inverse hyperbolic function…