15–48. Derivatives Find the derivative of the following functions.
y = 5^3t

Verified step by step guidance

1. Identify the function to differentiate, which is y = 5^(3t). This is an exponential function where the base is a constant (5) and the exponent is a linear function of t (3t).
2. Recall the derivative rule for exponential functions: if y = a^(u), where a is a constant and u is a function of x, then the derivative is given by dy/dx = a^(u) * ln(a) * (du/dx).
3. In this case, let u = 3t. Therefore, we need to find du/dt, which is the derivative of u with respect to t.
4. Calculate du/dt. Since u = 3t, the derivative du/dt = 3.
5. Now, apply the derivative rule: dy/dt = 5^(3t) * ln(5) * 3. This gives you the derivative of the function.