let's consider F(x)= \[a^x\]
on differentiating both sides w.r.t x we get \[\frac{\mathrm{d}{ } }{\mathrm{d} x} a^x\]= \[ a^x log_{e}(a)\]
On differentiating once again w.r.t x we get Dif\[\frac{\mathrm{d^2}{ a^x} }{\mathrm{d} x^2} \]=\[ a^x (log_{e}(a))^2\]
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Finally \[\frac{\mathrm{d^n}{ a^x} }{\mathrm{d} x^n} \]=\[a^x (log_{e}(a))^n\]
Problem. Find the value of 4th derivative of \[5^x\] at x=2 ?
Solution: \[\frac{\mathrm{d^4}{5^x } }{\mathrm{d} x^4} \]=\[5^x (log_{e}(5))^4\]=167.74011
