Question

find nth derivative of xlogx​

Answer 1

Answer:

aaaaaaaaaaaaaaaaaaaaaaaaaaaa

Answer 2

Given : xlogx​

To Find : nth derivative of xlogx​

Solution:

case 1 : logx is lnx

y = xlnx

y₁ = x (1/x)  + 1.lnx

=> y₁ = 1  + lnx

y₂ = 0  + 1/x

y₃ =  -1/x²

y₄ = (-1)(-2)/x³

y₅ = (-1)(-2)(-3)/x⁴

Hence yₙ = (-1)(-2)(-3).. .. .. ..(-n+2)/xⁿ⁻¹

=> yₙ = (-1)ⁿ⁻²(n-2)!/xⁿ⁻¹

case 2 : logx = lnx/ln 10

y = xlnx/ln 10

y₁ = x (1/x)/ln 10  + 1.lnx/ln 10

=> y₁ = 1/ln 10  + lnx/ln 10

y₂ =( 1/ln 10)(0  + 1/x)

y₃ = ( 1/ln 10)( -1/x²)

y₄ =( 1/ln 10) (-1)(-2)/x³

y₅ =( 1/ln 10) (-1)(-2)(-3)/x⁴

Hence yₙ = ( 1/ln 10)(-1)(-2)(-3).. .. .. .(-n+2)/xⁿ⁻¹

=> yₙ = (-1)ⁿ⁻²(n-2)!/xⁿ⁻¹.ln 10.

Learn More:

Find the derivative of the following functions from first principle. (i) x  

brainly.in/question/17176417

find the derivative of x²-cosx / sin xplease answe ​ - Brainly.in

brainly.in/question/15083061