Find the equation of the tangent to the curve y=2(e^x) at the point (0,2).

Q: 3 y (sinhx) + sinhx 3 4. step1 step2

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Q: On which derivative rule is integration by parts based?

A: Integration by parts is based on product rule of derivative. Mathematically, Product rule of…

Q: Find the nth-order derivative of the function y=arctanx at the point x=0.

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Q: How to solve for the derivative of Dy[tan(y)+1/tan(y)-1]? If it's 0, why?

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Q: y = 2 ||

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

Q: 1. у %3D х+/x

A: Topic = Derivative As per guidelines , At  a time only one question can be answered out of different…

Q: Find the derivative. 2 - - dy dx - if y(x) = 1 x + 3 dy dx ||

A: This question is based on Chain rule diffrentiation. d/dx{f(x).g(x)} = g(x)d/dx{f(x)} +…

Q: Discuss how the concept of instantaneous velocity v(t) can lead to the mathematical notion of a…

A: Topic:- application of derivatives

Q: Explain the derivatives and integration.

A: Solution: Derivatives: Definition of derivatives is , the rate of change of a quantity with respect…

Q: (x²+1)* V1-x y = In

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

Q: Use differentials to estimate the value. estimate =  exact value =

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Q: Find  y ″  by implicit differentiation. 2x3 − 5y3 = 5

A: We will differentiate w.r.t x twice using the product rule and the chain rule

Q: Use negative differential to obtain an equation of tangent curves at a given point.

A: Solve the following

Q: y=9 arctan (x+sqrt(1+x^2) )

A: ddx(xn)=nxn-1 ddxx =12x ddxtan-1(x)=1x2+1 Chain Rule: if f=f(u) where u is a function of x then…

Q: 2. Use logarithmic differentiation to find first derivative of y (sinx)r

A: Formula used: ddx[u(x)v(x)]= u(x)v(x).ddx[ln(u(x)).v(x)] ddx(u.v) =dudx.v + udvdx

Q: calculate the derivative y = tanh(ex )

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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 y''' (3rd derivative) of y = sin^2 (tan(6e^x))

A: Here,              We have given a function and we have to find its 3rd derivative.         So , the…

Q: 2.Find the derivative of y = In cosh x. %3D

A: Using chain rule of differentiation.

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

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Q: calculate the derivative with respect to x. ln x + ln y = x − y

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Q: Calculate the second derivative y : Vx - /y = 1

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Q: Calculate the derivative. 1 y = log 5x y' =0

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Q: Calculate the derivative of y=arctan√ex at x=0.

A: We differentiate both sides with respect to x using the chain rule.

Q: Find the slope of the tangent line to the curve x3 + y3 = 4xy at the point (2, 2). Use implicit…

A: According to question given that  We have to calculate the slope of the tangent line to the curve…

Q: find the equation of the tangent line to the graph of f(x) = x^3 + 3x^2 at the point (1, 4) without…

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Q: Shows the derivative function of: TC = Q³ + 2Q²  + FC(Q), where TC = Total Cost and FC = Fixed…

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Q: Find the derivative of y given that y = In (sinh x) %3D

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Q: Find the derivative of the function. y = tanh6(9x) %3D y' =

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Q: Calculate the derivative.

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Q: What is Newton's method in application of derivatives?

A: We have to write what is Newton's method

Q: Find the slope of the curve y = tan-!x at a1, b without calcu- 4 lating the derivative of tan-x.

A: Given y=tan-1x

Q: calculate the derivative y = ecosh−1 x

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

Q: The GoldPlus Company determines that the marginal cost for their Aiibe 64GB flash drive is given by…

A: One of the methods to solve a differential equation is by separating the variables and integrating…

Q: Find the equation of tangent and equation of normal for the implicit function y +3xy =x+y, at the…

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Q: Calculate the derivative at the point (0,0) of the function given by the equation x=y−2siny.

A: We differentiate both sides with respect to x

Q: Find an equation of the tangent line to x2 +xy – y³ = 7 at the point (3,2). (You must use implicit…

A:

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

A: Find the derivative of the function

Q: Find the equation of the line tangent to the graph of y = 6 ln(x) at x = 3. Tangent Line: y =

A: We have to find the slope of tangent at first.

Q: Determine the derivative of y. y = eV14x+6 %3D

A: Please refer the attached image for complete solution.

Q: How do you use Implicit differentiation find x^2+2xy−y^2+x=2 and to find an equation of the tangent…

A: The given equation is, x2+2xy-y2+x=2. Differentiate the given function with respect to x.…

Q: Find the equation of the tangent line to the curve given by f(x) = x2 ln x at the point  (1, 0)

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

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Q: Use implicit differentiation to calculate the value of derivative y' at the solution point (2, y) =…

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Q: Calculate the derivative of the function y=arccos x arctan x at x=0.

A: Differentiating with respect to x, we get

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

A:

Q: Find the values of x in the interval [0,2π] where the tangent line to the graph of y= sinxcosx is…

A: Given:y=sinxcosx,     [0,2π]

Q: Find and sketch an exponential equation of the form y = Cekx that passes through the points (0, 8)…

A: Given an exponential equation of the form y=Cekx that passes through the points (0,8) and (3,4). To…