Questions: If f(x)=2 * x^3-10 * x-12, find f'(x) d/dx(2 * x^3-10 * x-12)=

Solution Steps

To find the derivative \( f'(x) \) of the function \( f(x) = 2x^3 - 10x - 12 \), we differentiate each term individually using the power rule. The power rule states that if \( f(x) = x^n \), then \( f'(x) = n \cdot x^{n-1} \).

1. For the term \( 2x^3 \): \[ \frac{d}{dx}(2x^3) = 2 \cdot 3x^{3-1} = 6x^2 \]

2. For the term \( -10x \): \[ \frac{d}{dx}(-10x) = -10 \cdot 1x^{1-1} = -10 \]

3. For the constant term \( -12 \): \[ \frac{d}{dx}(-12) = 0 \]

Now, combine the derivatives of each term to get the derivative of the entire function: \[ f'(x) = 6x^2 - 10 + 0 = 6x^2 - 10 \]

Final Answer