Question

Differentiate the function with respect to tne inut ht=lnt/9+t³

Answer 1

To differentiate the given function, use the power rule and the sum rule. Differentiate each term separately and then combine the results.

Step-by-step explanation:

To differentiate the given function, we will use the power rule and the sum rule. Let's differentiate each term separately:

1. Differentiate lnt/9 using the power rule: d/dt (lnt/9) = 1/t * 1/9 = 1/(9t)

2. Differentiate t³ using the power rule: d/dt (t³) = 3t²

Now, combine the two results: d/dt (lnt/9+t³) = 1/(9t) + 3t²