Problem Set Problem 10 (1 point) Differentiate R(t)=(4t+e^t)(3-sqrt (t)) Answer: R'(t)=

Question

Problem Set Problem 10 (1 point) Differentiate R(t)=(4t+e^t)(3-sqrt (t)) Answer: R'(t)=

Answer 1

To differentiate the function \( R(t) = (4t + e^t)(3 - \sqrt{t}) \), we will use the product rule. The product rule states that if you have a function \( h(t) = f(t)g(t) \), then its derivative is given by:

Here, let:

First, we find the derivatives of \( f(t) \) and \( g(t) \):

Now, apply the product rule:

Substitute \( f(t) \), \( f'(t) \), \( g(t) \), and \( g'(t) \):

Simplify each term:

So, the derivative of \( R(t) \) is:

Soru

Problem Set Problem 10 (1 point) Differentiate R(t)=(4t+e^t)(3-sqrt (t)) Answer: R'(t)=

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