Question

How do you find the derivative of `5^x log_5 x`?

Answer 1

`(df)/(dx)=5^x/(xln5)+5^xlnx`

Explanation:

`f(x)=5^xlog_5x=5^xlnx/ln5`

Hence `(df)/(dx)=1/ln5[5^x xx1/x+lnx xx ln5xx5^x]`

= `5^x/(xln5)+5^xlnx`

[As `d/dx(5^x)=d/dxe^(ln5^x)=d/dxe^(xln5)=ln5e^(xln5)=ln5xx5^x`)