Question

Differentiate the following w.r.t.x. :

y = log e^_x3 log x³ 

Answer 1

Let y = (log e^_x3) (log x³) = (x³ log e)(log x³)

= x³ log x³    ...[∵ log e = 1]

= x³ (3 log x)

= 3x³ log x

∴ `("d"y)/("d"x) = "d"/("d"x) [3x^3 log x]`

= `3"d"/("d"x) (x^3 log x)`

= `3[x^3 "d"/("d"x) (log x) + (log x) "d"/("d"x) (x^3)]`

= `3[x^3 (1/x) + (log x)(3x^2)]`

= 3x² + 9x² log x

= 3x² (1 + 3 log x)