differentiate f(x) = log10(x^5 + 6)

Question

please differentiate f(x) = log10(x^5 + 6)

Answer 1

Question: differentiate f(x) = log10(x^5 + 6).

N.B. log_b(a) = log_d(a)/log_d(b), for any base d, with unknown a and b.

So, log_10(x^5 + 6) = log_e(x^5 + 6) / log_e(10), where e is the base of the natural logarithms

So, y = ln(x^5 + 6) / ln(10)

dy/dx = (1/ln(10))*(5x^4)/(x^5 + 6)