Question: 6) \( f(x) = 3x^3 - 5x^5 \)

Solution

To differentiate the function \( f(x) = 3x^3 - 5x^5 \), we will apply the power rule. The power rule states that if \( f(x) = ax^n \), then \( f’(x) = nax^{n-1} \). Differentiate each term separately: For the term \( 3x^3 \): The derivative is \( 3 \times 3x^{3-1} = 9x^2 \). For the term \( -5x^5 \): The derivative is \( -5 \times 5x^{5-1} = -25x^4 \). Combine the derivatives: \[ f’(x) = 9x^2 - 25x^4 \]