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Answer :
Final answer:
The derivative of the function [tex]y=5x^6+1.3x^10[/tex] is calculated using the power rule, resulting in [tex]30x^5 + 13x^9[/tex], which corresponds to choice A.
Explanation:
The question asks for the derivative of the function[tex]y=5x^6+1.3x^10[/tex]. To find the derivative, we apply the power rule, which states that the derivative of[tex]x^n is nx^(n-1)[/tex]. Therefore, we take each term of the function individually:
- For[tex]5x^6,[/tex] the derivative is [tex]5×6x^(6-1) = 30x^5.[/tex]
- For [tex]1.3x^10[/tex], the derivative is [tex]1.3×10x^(10-1) = 13x^9[/tex].
Combining these results, the derivative of the function is [tex]30x^5 + 13x^9[/tex], which matches choice A.
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