Find the nth derivative of 1/(x2+6x+8)
Answers
Answered by
2
Given:
y = 1 / (x²+6x+8)
To find:
The nth derivative
Calculation:
=> y = 1 / (x²+6x+8)
y = 1 / (x+2)(x+4)
y = 2[ 1/(x+2) - 1/(x+4) ]
Derivate both sides of the equation w.r.t x
=> y₁ = dy/dx = 2[ -1/(x+2)² + 1/(x+4)² ]
= -2[ 1/(x+2)² - 1/(x+4)² ]
Derivate both sides of the equation w.r.t x
=> y₂ = d²y/dx² = -2[ -2/(x+2)³ + 2/(x+4)³ ]
= 4[ 1/(x+2)³ - 1/(x+4)³ ]
Derivate both sides of the equation w.r.t x
=>y₃ = d³y/dx³ = 4[ -3/(x+2)⁴ + 3/(x+4)⁴ ]
= -12[ 1/(x+2)⁴ - 1/(x+4)⁴ ]
y_(n) = 2(-1)ⁿn![ 1/(x+2)ⁿ⁺¹ - 1/(x+4)ⁿ⁺¹ ]
Final answer:
The nth derivative is y_(n) = 2(-1)ⁿn![ 1/(x+2)ⁿ⁺¹ - 1/(x+4)ⁿ⁺¹ ]
Similar questions