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Answer :
Final answer:
The derivative of the function [tex]f(x)=-10x^7+3x^4[/tex] is found by applying the power rule to each term, resulting in [tex]-70x^6[/tex]for the first term and [tex]12x^3[/tex] for the second term, making option a) the correct answer.
Explanation:
The question asks us to find the derivative of the function [tex]f(x)=-10x^7+3x^4[/tex]. To find the derivative, we apply the power rule, which states that the derivative of [tex]x^n is nx^(n-1)[/tex]. Applying this rule to each term in the function:
- The derivative of [tex]-10x^7 is -70x^6[/tex] (multiplying the exponent 7 by the coefficient -10 and decreasing the exponent by 1).
- Similarly, the derivative of [tex]3x^4 is 12x^3[/tex] (multiplying the exponent 4 by the coefficient 3 and decreasing the exponent by 1).
Thus, the correct answer to the question is a) [tex]-70x^6 + 12x^3[/tex], representing the derivative of the given function.
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Final Answer:
The derivative of the function [tex]f(x) = -10x^7 + 3x^4 is -70x^6 + 12x^3.[/tex]Option a) is the correct answer.
Explanation:
The derivative of a function represents the rate of change of that function with respect to its variable. Calculating derivatives is fundamental in calculus to analyze functions and their behavior.
To find the derivative of the function f(x) = -10x^7 + 3x^4, we differentiate each term with respect to x using the power rule:
[tex]f'(x) =[/tex] [tex]d/dx[/tex] [tex](-10x^7)[/tex] + [tex]d/dx[/tex] [tex](3x^4)[/tex]
[tex]f'(x) = -70x^6 + 12x^3[/tex]
Therefore, the derivative of the function [tex]f(x) = -10x^7 + 3x^4[/tex] is -[tex]70x^6 + 12x^3[/tex]. Option a) is the correct answer.
