QuestionFind the derivative of the function $f(t) = e^{2t} \ln(t+1)$.

Studdy Solution
Combine the derivatives using the product rule:
$$f'(t) = u'(t) \cdot v(t) + u(t) \cdot v'(t)$$
Substitute the derivatives and functions:
$$f'(t) = (2e^{2t}) \cdot \ln(t+1) + (e^{2t}) \cdot \frac{1}{t+1}$$
Simplify the expression:
$$f'(t) = 2e^{2t} \ln(t+1) + \frac{e^{2t}}{t+1}$$
The derivative of the function is:
$$f'(t) = 2e^{2t} \ln(t+1) + \frac{e^{2t}}{t+1}$$