Question

Find fifth derivative of y = x3 log x​

Answer 1

y log = x^3

hope this will help u

Answer 2

Answer:

-6/x²

Step-by-step explanation:

y = x³*log x

diif.w.r.to.x,

dy/dx = 3x²log x + x³*1/x

= 3x²log x + x²

diff.w.r.to.x,

d²y/dx² = 6xlog x +3x²*1/x+2x

= 6xlog x + 5x

diff.w.r.to.x,

d³y/dx³ = 6log x + 6x*1/x + 5

= 6log x + 6 + 5

= 6log x + 11

diff.w.r.to.x,

d⁴y/dx⁴ = 0*log x + 6*1/x + 0

= 0 + 6/x + 0

= 6/x

= 6*x^(-1)

d⁵y/dx⁵ = 6*(-1*x^(-1-1))

= -6/x²

using formula

d/dx(x^n) = x^(n-1)

d/dx(log x) = 1/x