# What is the derivative of #f(x)=x*log_5(x)# ?

##### 1 Answer

Aug 6, 2014

When you're differentiating an exponential with a base other than

#f(x) = x * lnx/ln5#

Now, differentiate, and apply the product rule:

#d/dxf(x) = d/dx[x] * lnx/ln5 + x * d/dx[lnx/ln5]#

We know that the derivative of

#d/dxf(x) = lnx/ln5 + x/(xln5)#

Simplifying yields:

#d/dxf(x) = (lnx+1)/ln5#