Find the derivative of f(x) = log10 x.
We can rewrite this logarithm as
Since (ln 10) is a constant, the function f is a constant multiple of ln x:
We know how to find the derivative of this function:
Find the derivative of f(x) = log4 x2.
First, simplify the original function. We need to bring the exponent down in front, split up the logarithm, and combine all the constants into one:
Or, we could instead split up the logarithm first and then bring down the exponent (the order of these two operations doesn't matter):
Now we have a nicely rewritten function:
We've done an awful lot of work and haven't even started taking the derivative yet - but now, taking the derivative will be a piece of cake. The function f is a constant multiplied by ln x, therefore
We could make this even tidier by recognizing thatln 4 = ln (22) = 2ln 2,therefore
Make it rain.