**Consider: x=e(-sin-ly) Determine the point(s) in the first quadrant where the graph has horizontal tangent line.

Q: Find the derivative of the function.

A: To find: The derivative of the function . Formula used: Chain rule of derivative: Derivative of the…

Q: dy Find by implicit differentiation. Then find the slope of the graph at the given point. dx 3x³y =…

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Q: use implicit differentiction to find an equation of the tangent line to the graph of arctan (x+y) =…

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Q: Find the equation of the line tangent to y = 2sin x at x = p>2. Graph the function and the…

A: Given: Function y = 2sinx To Find: The equation of the tangent line at x = p  Concept Used: The…

Q: Find the slope of the tangent line to the given curve at the given value of x. Find the equation of…

A: Consider the provided curve, y=8-x2 and x=1. Find the equation of tangent line. First, we find the…

Q: Preview Use implicit differentiation to find the equation for the tangent line of x² + 2xy – y² + x…

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Q: Find the equation of the line tangent to the graph of y = 4 ln(x) at a = 2. Enter exact values.…

A: detailed solution is given below

Q: Find the derivative of the function y = tan(arcsin x)

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Q: Find the derivative

A: To compute the derivative of ln|cscx|

Q: 9-x Find the equation of the tangent line to the curve y = ln at (0, 0)? 9+x

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Q: equation of fhe tangent line to the curve + tan?x at Find an fixl=sec?x

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Q: Use technology (Desmos) to sketch a graph of y=tan⁡x for −π/2≤x≤π/2. From the graph determine the…

A: y = tanx

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: Find an equation of the tangent line to the curve at the given point. y = sin(sin(x)),  (2π, 0)

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Q: 356. [] Find the equation of the tangent line to the graph of æ – x Iny+ y = 2x + 5 at the point (2,…

A: Given: An equation, x3-xlny+y3=2x+5.

Q: the implicit differentiation to find slope and inclination of the tangent line to the graph of…

A: In this question, we have to use implicit differentiation to find the slope of the tangent. Along…

Q: Find the slope of the tangent line to the given curve at the given value of x. Find the equation of…

A: The slope of the tangent line is obtained by differentiating y, i.e., y' obtained is the slope of…

Q: Calculate the derivative. y = (In (cosh(x)))° (Use symbolic notation and fractions where needed.) dy…

A:

Q: Find equations for the lines that are tangent and normal to the graph of

A: Given equation of the function is: fx=tan xx Differentiating with respect to x we get, f'x=x…

Q: Find an equation of the tangent line to the graph of the function at the given point. You must write…

A: Equation of tangent line of the function y=f(x)  at the point (a,b) is y-b=f'(x)x=ax-a

Q: Find the slope of the tangent line to the given curve at the given value of x. Find the equation of…

A: Tangent line to a curve at a point is a line that "just touches" the graph of the curve at that…

Q: Find an equation of the tangent line to the curve at the point (2, 0). y = ln(x2 − 3)

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Q: III. Find the fifth derivative using product rule y = sin3xcos4x Where r is the last digit of your…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: Find the derivative: 7.) y = cot x

A: CotX is the ratio of Cosx and sinx

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

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Q: ャ〇 ५= Find derivative ( o y

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Q: y = In(arcsincosx); y

A: Given: y=lnsin-1cosx To find y' Solution: Chain rule of differentiation states that: ddxfgx=f'gx·g'x…

Q: etermine the equation of the tangent line to the graph of f(x) = O y = 6 + 6x y=-6x - 6 Oy=6-6x x

A: Topic:- application of derivatives and integration

Q: Find the equation of a tangent line to the curve y=xe2x at the point where x=1  Please show…

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Q: D/Dx (cosx)^x  slope of tangent function (cosx)^x at x=π/4

A: Given:- y = (cos(x))x To find:- Slope of tangent at x=π/4

Q: Can i get help step by step?

A: Given equation is as below Differentiate both sides of equation with respect to x

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: Find an equation of the tangent line to the curve at the given point. y = 9ex cos(x),    (0, 9)

A: y=9excosx Slope of the tangent line is the derivative of the given curve at the given point. So…

Q: Find the derivative. Simplify where possible  y = sinhcosh x

A: Our Aim is to find the derivative of the following function given below:-y=sinh(cosh x)

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: 20. Find the derivative: a) y=x' arctan x b) f(x) = arcsin(3x)

A: a) here we use product rule and power rule b) here we use basic arcsin(x) formula and chain rule

Q: Find an equation of the line tangent to the graph of f(x) = a) at (1,1); b) at c) at a) The equation…

A: Given: The graph of fx=1x6 To find the equation of tangent line at a) 1,1 b) 3,1729 c) -2, 164

Q: Calculate the derivative. y = ecoth (22x) (Use symbolic notation and fractions where needed.) dy dx

A: using chain rule

Q: 6 ind the slope of the tangent line to the curve y = (x- 35) at x= 6. Then write the equation of…

A: Given,         The tangent to the curve y=x2-356 at x=6.

Q: dy Use implicit differentiation to find dx x- cot(xy) = 1

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

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Q: 6use implicit differentiation to find the slope of the tangent line to the curve 8 arctan (x) +…

A: The slope of a curve f(x,y)=0 at a point (a,b) is given by, m=dydx(a,b)

Q: an equation of the tangent line to the curve at the point (2,

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Q: Find an equation of the tangent line to y = 16e* sec(x) at x = 77. (Use symbolic notation and…

A: In this question, we want to find the equation of the tangent line to the given curve at given…

Q: Consider the following. arctan(xy) = arcsin(7x + 7y) Use implicit differentiation to find the slope…

A: Given: tan−1(xy)=sin−1(7x+7y)

Q: Arctan /xy =1, find y'

A:

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

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.