Question 2 Differentiate the following functions (i) If y= e-t sin 4t, prove that +6+2y = 0. (ii) Given that sin(x? +y) = y (3x + 1), show that dy 2x cos(x? + y) – 3y² !3! dx 2y(3x + 1) – cos(x² + y)

Q: SOLVE THE EQUATION X = ex-1

A: The given equation is X=eX-1. Solve the equation. Here we use the formulas: lnab=blnalne=1

Q: Solve  5x =-5 3

A: Solve  5x =-5 3

Q: solve 6x-2.3x=-95.4

A: Consider the given equation.

Q: Solve

A: On solving

Q: Solve: a 5X-1 = 7x

A: We have to solve for x.

Q: The square of a positive number plus seven times the number 540. Find the number

A:

Q: –+l l5=405 %3D

A: We can solve the quinary number system problem as below.

Q: Find the value of the variable -5x = -5

A: Given equation is -5x=-5. To find the value of the variable. Solution: Multiplying both sides of…

Q: SOLVE 8-2y=4

A: Given that  8-2y=4               ⇒2y=8-4               ⇒2y=4                ⇒y=2…

Q: 近+5=2

A: The given equation is: 12x3+5=2 To simplify this algebraically, subtract 5 on the sides.…

Q: 5 . Solve: x - 3 21

A: We have to solve the equation: 5x-3≥1 Subtracting both sides 1, we get…

Q: Solve ex =-x

A:

Q: 42

A: We have to solve given equation for y.

Q: 4. Solve 6yx +2–12 = 18

A: Given : 6x+2 -12 =18

Q: Multiply the 1st equation by 2 to make -10y. 2x - 5y = -12 3x + 10y = 50

A:

Q: 4y+9=7y-12

A:

Q: Solve 3sin²x - 5tanx = 4

A: Given 3sin2x-5tanx=4

Q: V8x -23 + 18 = 25

A:

Q: Solve by elimination  4x + 10y= -30 2x-9y =27

A: Given,         4x+10y=-30         2x-9y=27

Q: olve ,  5x + 6y = 45 x + y = 5

A: