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

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Answer 1 · 2016-06-20T06:41:54

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

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

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

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

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

How do you find the derivative of 5^x log_5 x5^x log_5 x?