Applications of Derivative: Tangent and Normal Line 1. For x³ + y³ = 6xy, find the point where tangent line is horizontal

Q: the derivative of the function by using the rules of differentiation. f(u) = 20/ square root of U

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Q: Use the graph to estimate the slope of the tangent line to y = x" at the given point. Verify your…

A: We have to tell the slope of the tangents through the graphs. So, for that, we will differentiate…

Q: Estimate the slope of the tangent line of the function y(t) = v5t + 1 at the point t = 2. (Use…

A: Given: yt=5t+1 The slope of the tangent line at the point t=1 can be calculated as,…

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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: didfferential equation of tangents to x¯ = 4y

A: Solution is given as below:

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Q: dy - Use implicit differentiation to find the derivative dx . Find the slope of the curve at the…

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Q: Using implicit differentiation, find the slope of the tangent line to the graph of the curve x^4 +…

A: Slope of the tangent is obtained by dy/dx

Q: g) Use implicit differentiation to find y, given x' + y = 6xy in) Find the equation of the tangent…

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Q: (a) Use implicit differentiation to find an expression for (OR y') in terms of z and y. (b) Find the…

A: Differentiate y w.r.t. to x .

Q: Estimate the slope of the tangent line of the function y(t) = V2t + 1 at the point t 1. (Use decimal…

A: We have to find the first derivative in order to find slope.

Q: Can derivatives be used to find tangent lines of functions? If so, how would you do it?…

A: Yes derivatives are also used to find the tangent of the lines.The given function is,

Q: 3z-2x² -1 (2z–1)®

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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 derivative of the function. y = 9 tan-(x - V1+ x² ) ,2 y' =

A: The solution of the problem is given in the next step.

Q: Applications of Derivative: Tangent and Normal Line 1. For x3 + y3 = 6xy, find the point where…

A: The given equation is:x3+y3=6xyTo find the point where the tangent line is horizontal

Q: f(x) = 3 X at xo = 1

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Q: se implicit differentiation to find an equation of the tangent line to the curve.  x^2/3 + y^2/3 = 4…

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Q: A circle's central point is O(0, 0) and its radius is r, and its equation is x2 + y2 = r2 . What is…

A: The given circle has center at (x=4,y=0) and radius (r=2). The equation for this circle is-…

Q: Differentiate the function and find the slope of the tangent line at the given value of the…

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Q: f (x+h)-f(x) Using the definition of the derivative i.e. f'(x) = lim h→0 h a) Differentiate the…

A: First we will it's derivative then put x=2 then we will find tangent equation

Q: е. Find the slope of the curve y 4.x arccos(r - 1) at the point (1, 2m)

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Q: Find an equation of the tangent line to the curve y=3 arccos(x/2) at the point (1, pi

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Q: Find an equation of the tangent line to the curve y = 9" at the point (2, 81) . Tangent line: y =

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Q: An equation of the tangent and normal line to the curve Y-xesinx at (0, 0) is . www

A: Differentiate wrt x and us equation of tangent line

Q: Derivative of aresine Assume that y = sin x is a differentia- ble function of x. By differentiating…

A: Given: y=sin-1x

Q: Find an equation of the tangent line to the curve at the given point. y = sin(x) + cos(x),      (0,…

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Q: Estimate the slope of the tangent line of the function y(t) = V5t + 1 at the point t = 1. (Use…

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Q: (a) Using derivative as a slope find line that are tangent and normal to the following curve at the…

A: We know that equation of line with slope m and passing through the point (x0,y0) is     (y-y0)=…

Q: a. Use implicit differentiation to find the derivative b. Find the slope of the curve at the given…

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Q: Q: Using derivative as a slope, find the line that are tangent and normal to the following curve at…

A: the line that are tangent and normal to the following curve at the given point x2 + y2 = 25, (3, c)…

Q: Ise the derivative rules (shortcuts!) to find the equation of the tangent line at g = 4.

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Q: nd the point (both x and y coordinates) where the tangen

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Q: Use implicit differentiation to find the slope of the tangent line to the curve 2( + y) = 25(² – y²)…

A: The slope of the tangent line to the curve 2(x2+y2)2=25(x2-y2) at the point (3,1).

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 derivative of the function. y = etan(x)

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Q: 3. Use the implicit differentiation to find the equation of the tangent line to the curve x*y+ e =…

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Q: Use the graph to estimate the slope of the tangent line to y = xn at the given point. Verify your…

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Q: Use implicit differentiation to find the equations of the tangent and normal lines at the point (9,…

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Q: Find an equation of the tangent line to the curve y = 9"| at the point (2, 81). Tangent line: y

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Q: Find the derivative y = x arctan x

A: We know that in derivative y=u v and derivative of it is given by dydx=udvdx+vdudx

Q: Using the definition, find the derivative of function 2z-i 1 (z)= at the point z = = -¡. z + 2i

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Q: Find the slope of the tangent line of f(x

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Q: Implicit differentiation Use implicit differentiation to finddy/dx.

A: Implicit differentiation is used to find the differentiation of the functions containing more than…

Q: Find the equation of the tangent line to the curve y=xlnx that is parallel to the line Y=1+3x.

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Q: What is the defintion of a derivative? Usng the definition of a derivative at a given point, find…

A: Definition of Derivative:The derivative of a function of a real variable measures the…

Q: Find the derivative of the function y 2 sec- (x + 2). %3D (Use symbolic notation and fractions where…

A: To find the derivative of:y=2sec-1x+2