High School

Find the derivative of [tex]f(x) = -10x^7 + 3x^4[/tex].

What is the derivative of the given function?

A) [tex]-70x^6 + 12x^3[/tex]
B) [tex]-10x^6 + 12x^3[/tex]
C) [tex]-70x^6 + 3x^3[/tex]
D) [tex]-10x^6 + 3x^3[/tex]

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).

  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).
  2. 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.