Answer :
To find the derivative of the expression [tex]\(-9x^4 + 3x^8\)[/tex], we will differentiate each term separately using the power rule. The power rule states that if you have a term in the form of [tex]\(ax^n\)[/tex], its derivative is [tex]\(a \cdot n \cdot x^{n-1}\)[/tex].
Let's apply this to each term in the expression:
1. Differentiate the first term [tex]\(-9x^4\)[/tex]:
- According to the power rule, the derivative is [tex]\(-9 \cdot 4 \cdot x^{4-1} = -36x^3\)[/tex].
2. Differentiate the second term [tex]\(3x^8\)[/tex]:
- Again, using the power rule, the derivative is [tex]\(3 \cdot 8 \cdot x^{8-1} = 24x^7\)[/tex].
Now, combine the derivatives of both terms to get the derivative of the whole expression:
The derivative of [tex]\(-9x^4 + 3x^8\)[/tex] is [tex]\(24x^7 - 36x^3\)[/tex].
So the final derivative is:
[tex]\[ 24x^7 - 36x^3 \][/tex]
Let's apply this to each term in the expression:
1. Differentiate the first term [tex]\(-9x^4\)[/tex]:
- According to the power rule, the derivative is [tex]\(-9 \cdot 4 \cdot x^{4-1} = -36x^3\)[/tex].
2. Differentiate the second term [tex]\(3x^8\)[/tex]:
- Again, using the power rule, the derivative is [tex]\(3 \cdot 8 \cdot x^{8-1} = 24x^7\)[/tex].
Now, combine the derivatives of both terms to get the derivative of the whole expression:
The derivative of [tex]\(-9x^4 + 3x^8\)[/tex] is [tex]\(24x^7 - 36x^3\)[/tex].
So the final derivative is:
[tex]\[ 24x^7 - 36x^3 \][/tex]
