y = V(1 + x3}² 1/3

Q: Second derivatives Find y′′ for the following functions. y=xsin(x)

A: Here given function, y=xsin(x) and we have to find the second derivatives of the given function.…

Q: Homogenoys Equations: Evaluate the DE xdy+(2y-x)dx=0

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Q: please find the first and second derivatives and show complete solution

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Q: H (t) = 3csch (t) + 7 sinh(t)

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Chain Rule with several independent variables Find the following derivatives. zs and zt, where z =…

A: Given, z = sin (x)cos (2y) x = s+ t  y = s - t

Q: Implicit Differentiation To find y' given f(x,y) = 0: 1. Differentiate both sides of the equation…

A:

Q: Derivatives of functions with rational exponents Find dy/dx

A: We have to find the derivative dydx of the function: y=5x+123 We know the formula of derivatives,…

Q: DERIVATIVES of ALGEBRAIC FUNCTIONS dy or y' of the following functions in terms of x. Determine dx…

A: Given,y=x2+153x-2-113differentiating both the sides w.r.t. xdydx=ddxx2+153x-2-113using product…

Q: dx 7. x²+6x+8 dx 8. V5x²–15 100 – 49x² dx 9.

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Q: -1 csch (tanx)

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Q: Derivatives from a graph Let F = ƒ + g and G = 3ƒ - g,where the graphs of ƒ and g are shown in the…

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Q: Formula for slope: f(x + h) – f(x) m = lim h→0 h 1. Given the function: f(x) = x² + 2x + 1 where x =…

A: The given function f(x)=x2+2x+1 , x=3m=limh→0f(x+h)-f(x)h

Q: CHAIN RULE DERIVATIVES Date Directions: Differentiate the given functions. 2.) G(X) - T52"

A:

Q: DERIVATIVES of ALGEBRAIC FUNCTIONS or y' of the following functions in terms of x. dx dy Determine…

A: Derivative of the given function: y=1-x+1-x

Q: Tangent lines The line tangent to the curve y = h(x) at x = 4 isy = -3x + 14. Find an equation of…

A: We have given tangent line to the curve y=hx at x=4 is y=-3x+14 .

Q: Differentials Consider the following function and expressthe relationship between a small change in…

A: Given that, f(x)=x+44-x

Q: Tangent Line. If p(x) : 2x2 + 6х3 + + 4 (a) Then p'(1) = (b) The equation of the tangent line to the…

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Q: definite integral* (b=3) (a=-3)   (e^-0.2x)*(9-(x^2)) dx (in terms of pi if possible)

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Q: derivative to identify 10. Use the test the intervais function glx) = x 4 - 4x% +4x² is where the…

A: To find the local minima and maxima

Q: Derivative formulas Derive the following derivative formulas given that (cosh x) = sinh x and - dx…

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Q: Derivative formulas Derive the following derivative formulas given that (cosh x) = sinh x and - dx…

A: The derivative of sechx have to be found. ddxsechx since sechx is the reciprocal of coshx, This can…

Q: Derivatives of constant multiples of functions Evaluate the followingderivatives.

A: Given: a ddx-7x118(b) ddt38t

Q: Ssinh(3x-1) dx 10.

A:

Q: xy = e2*; y ху e2x; y

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Q: integrating factor (find it by inspection). Also, determine the corresponding particular solution…

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Q: Derivatives of power and constant functions Evaluate the followingderivatives.

A: Given : a. ddxx9b. ddxxc. ddx28

Q: Implicit and logarithmic differentiation Find the first derivative R(t)=[Sin(4t)]^6t

A:

Q: f(x)= (25x^2 +81)/x a. find the critical values of the function. b. use the First Derivative Test…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Differentiation the function y = sin( – 6x)cot(- 7x) y' = %D

A: The function is given as , y=sin-6xcot-7x find y'.

Q: Integration of Rational Functions of Sine and Cosine #4

A: We have to find the integral.

Q: arctan x Suppose that f is differentiable at 0 and f(0) = 5. Find the derivative of at x = 0. f(x)

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Q: Derivatives of power and constant functions Find thederivative of the following functions.

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

Q: Inconclusive tests Show that the Second Derivative Test is inconclusive when applied to the…

A: To show second derivative test is inconclusive.

Q: ANTI-DERIVATIVES OF TRIG FUNCTIONS Please find f(x) and f'(x) of f''(x)=-4sin(2x). Please show…

A: f"x=-4sin2x ⇒ ddxf'(x)=-4sin2x . Therefore,…

Q: I. Matching Type Direction: Match Column A with Column B. 1. e* a. cos x +i sin x b.-+-+.+(-1)-1 b.-…

A: We need to match column A with column B:

Q: Derivatives of power and constant functions Evaluate the followingderivatives.

A: We have to find the derivatives of the functions: a.  ddxx9b.  ddxxc.  ddx28 We know the formula of…

Q: 3x* 1. 4x2 –3x+5 -2x²+5 2. 2cos(30²)

A:

Q: 2. Integration is the reverse process of differentiation. When we differentiate we start with an…

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Q: Chain Rule with several independent variables Find the following derivatives. zs and zt, where z =…

A: Given: z = sin2x+y, x = s2-t2,  y = s2+t2 To find: The derivatives zs  and  zt .

Q: (Implicit differentiation) dy Find from the following expressions dx (a) x = y sinh 4x+ cosh y (b) y…

A: (a) First calculate the the value for dx/dy. Then, determine the value for dy/dx by using reciprocal…

Q: Derivatives of constant multiples of functions Evaluate the followingderivatives

A: Consider the expression ddx-7x118 ddx-7x118=-78ddxx11=-7811x11-1=-77x108

Q: 3. f (x) = V1+ v1 – x 4. у %3

A:

Q: 3. y = cot(x + 2) cosh(x + 2)

A: Given: y=cot(x+2) cosh(x+2)                                  Here, cosh(x+2) is hyperbolic function…

Q: A critical value such that f"(x)=0is called a stationary point. a) Show that both of the functions…

A: We have to find critical (stationary) points, maxima or minima and concavity.

Q: DERIVATIVES of ALGEBRAIC FUNCTIONS dy or y' of the following functions in terms of x. dx Determine…

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Q: 1 2. Find the derivative of y =V1 - x2 +arcsin x 2°

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Q: Total differential. We have f (x, y) = ln (x² + y²) at the point (1, 2). %3D NO CALCULATOR. Evaluate…

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Q: The Reciprocal Rule a. The Reciprocal Rule says that at any point where the function v(x) is…

A: Given: (a) The quotient rule is given as,

Q: Derivatives involving ln x Find dy/dx for the following functions

A: Derivatives involving ln x Find dy/dx for the following functions   " Since you have posted a…

Q: DERIVATIVES OF ALGEBRAIC FUNCTIONS Determine or y' of the following functions in terms of x. dx 2. y…

A: Given equation: y=x2+153x-2-113

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: