Question: 1. -1 3. What is $\frac{d}{dx}(12x^{-12} - 6x^7 - x)$? - $-144x^{-11} + 42x^6 - 1$ -…

1. -1

2. What is $\frac{d}{dx}(12x^{-12} - 6x^7 - x)$?

• $-144x^{-11} + 42x^6 - 1$

• $-144x^{-11} + 42x^6$

• $-144x^{-11} + 42x^6$

Solution

To find the derivative \(\frac{d}{dx}(12x^{12} - 6x^7 - x^7)\), we will differentiate each term separately. Start with the first term \(12x^{12}\). Differentiate it: \[ \frac{d}{dx}(12x^{12}) = 12 \cdot 12x^{11} = 144x^{11} \] Next, differentiate the second term \(-6x^7\). Differentiate it: \[ \frac{d}{dx}(-6x^7) = -6 \cdot 7x^6 = -42x^6 \] Finally, differentiate the third term \(-x^7\). Differentiate it: \[ \frac{d}{dx}(-x^7) = -1 \cdot 7x^6 = -7x^6 \] Now, combine all the derivatives: \[ 144x^{11} - 42x^6 - 7x^6 \] Combine like terms: \[ 144x^{11} - 49x^6 \] So, the derivative is: \[ 144x^{11} - 49x^6 \] This simplifies to match the option closest in the provided choices, but there is a minor discrepancy; it seems like the options have a small error in one of the powers. The closest form is consistent with the calculations provided but none perfectly match the answer due to a likely error in the options or setup. Please verify the options.