What is the derivative of f(x)=5^x log6(x)?

Answer 1

Exponential rule:
d(a^x)/dx = ln(a) a^x

For logarithms to arbitrary base:
d(log_a(x))/dx
=d(ln(x)/ln(a))/dx
=ln(a)/x

Finally, the product rule:
d(uv)/dx = u dv/dx + v du/dx

set
u=5^x,
v=log₆(x)
=ln(x)/ln(6)

Can you take it from here?

Answer 2

For logarithms to arbitrary base:
d(log_a(x))/dx
=d(ln(x)/ln(a))/dx
=1/(ln(a)*x)