Question

Differentiate f(y) = 1 y² - 3 y⁴ (y⁹y³).

Answer 1

To differentiate the given function, f(y) = 1 y² - 3 y⁴ (y⁹y³), follow these steps: simplify the function, differentiate each term, and combine the derivatives to get the final result.

Step-by-step explanation:

To differentiate the given function, f(y) = 1 y² - 3 y⁴ (y⁹y³), we need to apply the rules of differentiation. Let's break it down step by step:

1. First, simplify the function by multiplying the terms: f(y) = y² - 3y⁴y¹²y³³
2. Next, differentiate each term one by one by using the power rule, chain rule, and product rule if necessary. For the first term, y², the derivative is 2y. For the second term, -3y⁴y¹²y³³, we can simplify it to -3y¹⁶y⁶ by adding the exponents. The derivative of this term is -48y¹⁵y⁵.
3. Finally, combine the derivatives of each term to get the final derivative of f(y). In this case, the derivative is: f'(y) = 2y - 48y¹⁵y⁵