<Dd> y ′ (x) = y (x), (\ displaystyle y' (x) = y (x),) </Dd> <P> satisfying the initial condition y (0) = 1 (\ displaystyle y (0) = 1). </P> <P> Based on this characterization, the chain rule shows that its inverse function, the natural logarithm, satisfies (log e ⁡ y) ′ = 1 / y (\ displaystyle (\ log _ (e) y)' = 1 / y) for y> 0 (\ displaystyle y> 0), or log e ⁡ y = ∫ 1 y 1 t d t (\ displaystyle \ log _ (e) y = \ int _ (1) ^ (y) (\ frac (1) (t)) \, dt). This relationship leads to a less common definition of the real exponential function exp x as the solution y to the equation </P> <Dl> <Dd> x = ∫ 1 y 1 t d t (\ displaystyle x = \ int _ (1) ^ (y) (1 \ over t) \, dt). </Dd> </Dl>

Is the square root of x an exponential function