Find \frac{d^{9}}{dx^{9}}(x^{8}\ln x).

sodni3

sodni3

Answered question

2021-10-03

Find d9dx9(x8lnx).

Answer & Explanation

tabuordg

tabuordg

Skilled2021-10-04Added 99 answers

Step 1
To obtain d9dx9(x8lnx).
Compute the derivatives.
ddx(x8lnx)=x7+8x7lnx
d2dx2(x8lnx)=(x7+8x7lnx)=7x6+8x6+56x6lnx=15x6+56x6lnx
d3dx3(x8lnx)=(15x6+56x6lnx)=90x5+56x5+336x5lnx=146x5+336x5lnx
d4dx4(x8lnx)=(146x5+336x5lnx)=730x4+336x4+1680x4lnx
=1066x4+1680x4lnx
d5dx5(x8lnx)=(1066x4+1680lnx)=5944x3+6720x3lnx
Step 2
d6dx6(x8lnx)=24552x2+20160x2lnx

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