del ateb ea ezt = e^(cob te Sinb) %3D e atcb e Note %3D e

Q: Explain how to apply the First Derivative Test.

A: Explain how to apply the First Derivative Test.

Q: cosh(3x²y) = ln(e*y + 1)

A: Differentiate the cosh3x2y=lnexy+1 with respect to x. dcosh3x2ydx=dln(exy+1)dx Use the chain rule…

Q: 1+ln(3x²) y = 1+ln(4x) ||

A: Given function - y = 1+ln3x21+ln4xDifferentiating on both sides with respect to x - dydx =…

Q: The deferential of point functions are exact differentials. Select one: True False

A: True

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: Calculate the derivative indicated.

A: given,        A=dPdVV=-2     where P=7/V

Q: Give a discussion as to why differentiation and integration are inverse processes. You should…

A:

Q: Find the derivative. Simplify where possible. y  = Cosh-1 √x

A:

Q: Explain the derivatives and integration.

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

Q: y Arctar 3-V9-x2

A: Given: y=tan−1x3−9−x2 To find: the second derivative of the function

Q: In y - Р(у) - %3D ey

A: We will use division rule and standard formulas to find required derivatives

Q: Find dy/dt thru logarthmic differentiation (apply logarithm on both sides of the equation.

A:

Q: Explain the concept of differentiation and integration.

A: Differentiation and integration are the process of calculus in mathematics. In differentiation, we…

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

A: Solve the following

Q: b. y = cosh(arctan 3x)

A: Given: y=coshtan-13x We know that ddxcoshx=sinhx                                              ..1

Q: =) Give a discussion as to why differentiation and integration are inverse processes. You should…

A:

Q: he surface al derivative

A:

Q: How can you relate antiderivatives as an opposite of derivatives in your life? explain

A: Solution is given below:

Q: Xyz. %3D Use implicit differentiation to find az/ar

A: The given function is ez=xyz.

Q: Find the derivative of y = tan 3x

A: Given function is: y = tan 3x We have to find the derivative of y with respect to x.

Q: An open cylinder can has an inside radius of 2cm and an inside height of 5cm. use the total…

A: We will estimate the volume of cylindrical metal as following. Inside radius = 2 cm Inside height =…

Q: Find the derivative of the trigonometric function.

A: To Determine: The derivative of y=sinπx

Q: calculate the derivative y = tanh(ex )

A:

Q: 2. Arcsin(x/y) = 4x + 3y %3D

A:

Q: What are the formulas for differentiation and integration? How are they applied?

A: To write: Formulas for differentiation and integration.

Q: what is the first derivative of arccos4x

A:

Q: Describe the Second Derivative Test in your own words

A: A second derivative test is conducted to find the relative maxima and  minima of a given function.

Q: Which derivative rule is used to derive the Integration by Parts formula?

A:

Q: This is determined by the largest derivative, or the highest level of differentiation, present in a…

A: We have to check

Q: Find dy ldx by Tmplicit differentiation. tanLx-y)=

A:

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

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

Q: Find the derivative of y = sin (cot(3x)) %3D

A:

Q: ャ〇 ५= Find derivative ( o y

A:

Q: Find the derivative of the cotangent function y=cotx

A:

Q: y = cos(cosh(cos x)))

A: Given function is, y=coscoshcosx. It is differentiated as follows: Apply the chain rule:…

Q: Find oy y'

A: We have to find

Q: Find the derivative of y = etan x %3D

A: Giveny=etanxTo findderivative of y.

Q: Find the first derivative in the form of dy/dx  y=(3x-2) sq rt(3x-2) please show all your work so…

A:

Q: ex + siny = cos(x³y²) %3D

A:

Q: а. у %3D sinh(3x? In (1 + 3Vx))

A: We have to use chain rule here.

Q: Find the derivative of y = arctan(x² + 3)

A: To find: The derivative of y=tan-1x2+3. Formula used: Chain rule of derivative: fgx'=f'gx·g'x Power…

Q: Find the first derivative of y = (In x)"

A: The differentiation of nested form of function is calculated using the chain rule of…

Q: 7. y cot (sin 0) %3D

A: on doing differentiation we get

Q: Find the derivative of the function. y = cot2(sin(0)) y' = %3D

A: According to guidelines we should have been able to solve only first one question at a time # first

Q: a Write down the derivative of arcsinx. b Use integration by parts to find | arcsinx d.x.

A: a. Derivative of arcsin(x) is given by ddx(arcsin(x)) = ddx(sin-1(x)) = 11 - x2

Q: Y = 2 Arccos ( 1 -) + v4x – x²

A:

Q: y = cos /sin(tan Tx) %3D

A:

Q: 5. Find the 25" derivative of y= In x.

A: We have to find the 25th derivative of y=ln(x)

Q: 33. Зе - х%3D 0, (3,0)

A: