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Answer :
Final answer:
The derivative of the function f(x)=-10x^7+3x^4 is found by applying the rule for derivatives of power functions, resulting in -70x^6 + 12x^3, which corresponds to answer A) -70x^6 + 12x^3.
Explanation:
The question asks for the derivative of the function f(x) = -10x^7 + 3x^4. To find the derivative, we apply the rule that the derivative of x^n is n*x^(n-1).
- For the term -10x^7, applying the rule gives us -70x^6 (multiplying the exponent 7 by the coefficient -10 and decreasing the exponent by 1).
- For the term 3x^4, we obtain 12x^3 (multiplying the exponent 4 by the coefficient 3 and reducing the exponent by 1).
Combining these results gives us the derivative of the function as -70x^6 + 12x^3. Therefore, the correct answer is A) -70x^6 + 12x^3.
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