Derivative of a Vector Valued Function

The derivative is $\langle e^{t},\frac{1}{\ln(t+1)} \rangle$.

The derivative is $\langle e^{t},\frac{1}{t+1} \rangle$.

The derivative is $\langle e^{t},\frac{d}{dt}\ln(t+1) \rangle = \langle e^{t},\frac{1}{t} \rangle$.

The derivative is $\langle e^{t},\ln(t+1) \rangle$.