Let r(w) = 5^w + logsub4w

Question

Evaluate r'?

Answer 1

The equation is r(w) = 5^w + log₄ w.

r(w) = 5^w + log₄ w.

Apply base rule of logarithm : log_b a = log a/log b.

r(w) = 5^w + (log w/log 4).

Derivative the above equation with respect to w.

r ' = (5^w)' + (log w/log 4)'

Derivative of a^x is a^x log a,

r ' = 5^wlog 5 + [(1/log 4)(log w)']

Derivative of log x is 1/x.

r ' = 5^wlog 5 + [(1/log 4)(1/w)]

r ' = 5^wlog 5 + [1/(wlog 4)].

Therefore,  r ' = 5^wlog 5 + [1/(wlog 4)].