23–26 Use a calculator or CAS to evaluate the line integral correct to four decimal places. 23. SF• dr, where F(x, y) = xy i + sin yj and r(t) = e'i + e j, 1

Q: dy Use implicit differentiation to find given dr tan(x + 2y) + cos y = x² – y²

A: From the given problem;   tanx+2y+cosy=x2-y2   Now differentiating with respect to x.…

Q: y' = x - 2y cot(2x)

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Q: 13. Find y' for sin(xy²) + x² = y². %3D

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Q: z + 2.5 -3 = Z

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Q: y becomes 4. Show that dx y"-2 xy'+A y=D0

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Q: 3. Find f(x) if f'(x) = sec²x - sinx and f(TT/4) = 1. %3D %3D

A: Given: f'(x) = sec2x -sinx  To find: The value of f(x)  and  fπ4.

Q: 7. Differentiate w.r.t x- sin 5x cos 3x 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

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Q: 4. 0 t² sin 2t dt

A: Given query is to find the value of the integral.

Q: Suppose the curve y = f(x) passes through the origin and the point (1,1). Find the value of the…

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Q: Find by implicit differentiation for x2+y2=25 at point P(0,5).

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Q: 3. Show that sinh a + sinh y = 2 sinh cosh %3D

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Q: Find f. f "(t) = 5e + 8 sin t, f(0) = 0, f(x) = 0 f(t) :

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Q: - Differentiate the function (find F'(x)) if F(x) = sin(t² + 1) dt

A: Apply Leibnize's. Rule

Q: x2 sin3(x) Find ax if y = In \cos(x*).V1+x,

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Q: x+y are functions of t.Ue %3D Ronphicit differentiation to express in terms af dx X and y dy

A: Explanation of the solution is given below....

Q: Let y = sin (x + y), find y'.

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Q: 5. Use implicit differentiation to find y'. a) хеУ 3 х — у

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: How can y = ex in the vicinity of x = 0 (with appropriate labels) be sketched?

A: To sketch the graph of y=ex in the vicinity of x=0, follow these steps: 1. Understand the Basic…

Q: Find f. 13 f"(x)=x³+ sinhx, f(0) = 4, ƒ(2)= 5

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Q: dy 4) Find by implicit differentiation, where dx y5 + x²y° = x* + y.

A: The objective is to find dy/dx by implicit differentiation

Q: 6. Find the arclength of the curve y Note: L = 1+ (f'(x))² dx √ 1 x²+1 for -2 ≤ x ≤ 2.

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Q: Use implicit differentiation to find dz/ yz = 5 In(x + z) az dz dy II

A: The given equation is yz=5lnx+z Differentiate the given equation partially with respect to x.…

Q: cosh x dy + (y sinh x + ex) dx = 0

A: Step 1:

Q: What is dy/dt of the given? Show both the simplified and unsumplified answer.

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Q: b.9f Fex)=x Sin lgix), where gL1)= , and g' (1)= -1, then f'(1)=2

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Q: 1- find dy/dx as a function of x. y = sec (tan x)

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.