Question: (\frac{d}{dx}(12x^{12} - 6x^7 - x)\)…

\(\frac{d}{dx}(12x^{12} - 6x^7 - x)\)

Solution

Find the derivative of the function \( f(x) = 12x^{12} - 6x^7 - x \). Apply the power rule, which states that the derivative of \( ax^n \) is \( anx^{n-1} \). Differentiate each term separately: \[ \frac{d}{dx}(12x^{12}) = 12 \cdot 12x^{11} = 144x^{11} \] \[ \frac{d}{dx}(-6x^7) = -6 \cdot 7x^6 = -42x^6 \] \[ \frac{d}{dx}(-x) = -1 \] Combine the derivatives: \[ f’(x) = 144x^{11} - 42x^6 - 1 \] The derivative of the function is \( 144x^{11} - 42x^6 - 1 \).