Question
Given that y = Γ(2x + 1)*, show that dy = (2x + 1)" (Ax + B) dx where n, A and B are constants to be found.
58
likes288 views
Answer to a math question Given that y = Γ(2x + 1)*, show that dy = (2x + 1)" (Ax + B) dx where n, A and B are constants to be found.
Cristian
4.7119 Answers
1. Differentiate y = x(2x + 1) with respect to x.
2. Set the result equal to (2x + 1) (Ax + B).
Let's go through the steps:
1. Π£ = x(2x + 1)
Apply the product rule: Y = (2x + 1) + x (2)
2. Simplify the derivative:
3=22+1+22
3. Combine like terms:
Π£ = 4x + 1
Now, set this equal to (2x + 1) (Ax + B):
4x + 1 = (2x + 1)(Ax + B)
Expand the right side:
4x + 1 = 2Ax% + (2A + B)x + B
Now, match coefficients:
1. Coefficient of x?: 2A = O implies A = 0
2. Coefficient of x: 2A + B = 4 implies B = 4
3. Constant term: B = 1
so, A = 0 and B = 4. The expression for dy/ d is:
dy/dx = (2x + 1)(Ax + B) = (2x + 1)(4x + 4
Frequently asked questions (FAQs)
What is the length of the hypotenuse of a right triangle if the opposite side measures 10 units and the adjacent side measures 15 units?
+
What is the value of the derivative of f(x) = 3x^4 + 2x^3 - 5x^2 + 7x - 1 at x = 2?
+
What is the value of x in the equation log(base 5) x = 3?
+
New questions in Mathematics