# Ex 5.4, 10 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at April 16, 2024 by Teachoo

Last updated at April 16, 2024 by Teachoo

Ex 5.4, 10 Differentiate w.r.t. π₯ in, cosβ‘(logβ‘π₯ + π^π₯), π₯ > 0Let π¦ = cosβ‘(logβ‘π₯+ π^π₯ ) Differentiating both sides π€.π.π‘.π₯ π¦^β² = (cosβ‘(logβ‘π₯ + π^π₯ ) )^β² π¦^β²= γβsin γβ‘(logβ‘π₯+π^π₯ ) (logβ‘π₯ + π^π₯ )^β² π¦^β²= γβsin γβ‘(logβ‘π₯+π^π₯ ) ((logβ‘π₯ )^β²+(π^π₯ )^β² ) π¦^β² = γβ sin γβ‘(logβ‘π₯+π^π₯ ) (1/π₯ + π^π₯ ) π^β² = ββ‘(π/π + π^π ) πππ (πππβ‘π + π^π )