Find the derivative of \( y=5 x^{9}+8^{x}+24 \) \( \frac{d y}{d x}= \)

1. Write the function: \[ y = 5x^9 + 8^x + 24 \] 2. Differentiate each term with respect to \( x \): - For the first term \( 5x^9 \), use the power rule: \[ \frac{d}{dx} (5x^9) = 5 \cdot 9x^{9-1} = 45x^8 \] - For the second term \( 8^x \), use the derivative rule for exponential functions: \[ \frac{d}{dx} (8^x) = 8^x \ln(8) \] - For the constant \( 24 \), the derivative is: \[ \frac{d}{dx} (24) = 0 \] 3. Combine the results: \[ \frac{dy}{dx} = 45x^8 + 8^x \ln(8) \]