Choose the correct answer from the drop-down menu. Find h(x) for the function H' * (x) = d/dx ((5x ^ 6 + 2x ^ 4)/(x ^ - 3)) 45x ^ 5 + 14x ^ 5 h(x)= (5 * x deg + 2x ^ 4)/(x ^ - 5) -

To find \( h(x) \), we need to evaluate the given derivative and then solve for \( h(x) \).

Given:
\[
H'(x) = \frac{d}{dx}\left(\frac{5x^6 + 2x^4}{x^{-3}}\right) = 45x^5 + 14x^5
\]

1. **Simplify the expression for \( H(x) \):**
   \[
   \frac{5x^6 + 2x^4}{x^{-3}} = (5x^6 + 2x^4) \cdot x^3 = 5x^9 + 2x^7
   \]

2. **Differentiate \( H(x) \) to find \( H'(x) \):**
   \[
   \frac{d}{dx}(5x^9 + 2x^7) = 45x^8 + 14x^6
   \]

Since this matches the right-hand side given as \( H'(x) = 45x^5 + 14x^5 \), there appears to be an inconsistency with the problem statement because \( H'(x) \) should be written as \( 45x^8 + 14x^6 \) based on standard differentiation.

For \( h(x) \), if we assume the function is:
\[
h(x) = \frac{5x^{\text{deg}} + 2x^4}{x^{-5}},
\]
we need clarification on what "deg" means here. If "deg" is meant to represent the degree of \( x \), we need to specify which term is used. Can you clarify or adjust the problem statement for accuracy?

Would you like further breakdown or review of other parts of the problem?

Choose the correct answer from the drop-down menu. Find h(x) for the function H'(x) = d/dx ((5x^6 + 2x^4)/(x^-3)) = 45x^5 + 14x^5. h(x) = (5 * x^deg + 2x^4)/(x^-5).

Explore how to find h(x) for the given derivative problem H'(x) = d/dx ((5x^6 + 2x^4)/(x^-3)) = 45x^5 + 14x^5. The solution includes simplifying rational functions, applying the power rule, and understanding differentiation concepts. Ideal for students in Grades 11-12.

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