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

Transcript text: If $f(x)=2 \cdot x^{3}-10 \cdot x-12$, find $f^{\prime}(x)$ $\frac{d}{d x}\left(2 \cdot x^{3}-10 \cdot x-12\right)=$

Solution

Solution Steps

Step 1: Differentiate each term separately

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 $f'(x) = n \cdot x^{n-1}$ .

Step 2: Apply the power rule to each term

For the term $2x^3$ : $\frac{d}{dx}(2x^3) = 2 \cdot 3x^{3-1} = 6x^2$
For the term $-10x$ : $\frac{d}{dx}(-10x) = -10 \cdot 1x^{1-1} = -10$
For the constant term $-12$ : $\frac{d}{dx}(-12) = 0$

Step 3: Combine the derivatives

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

$\boxed{f'(x) = 6x^2 - 10}$

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