Calculus exam Find the derivation of each of the following expression 3x3+2x+3/2x solve in English

Using the power rule $\frac{d}{dx}(ax^n) = anx^{n-1}$:

$$\frac{d}{dx}(3x^3) = 3 \cdot 3x^{3-1} = 9x^2$$

Using the power rule $\frac{d}{dx}(ax^n) = anx^{n-1}$ (where $n=1$):

$$\frac{d}{dx}(2x) = 2 \cdot 1x^{1-1} = 2x^0 = 2 \cdot 1 = 2$$

Using the power rule $\frac{d}{dx}(ax^n) = anx^{n-1}$:

$$\frac{d}{dx}\left(\frac{3}{2}x^{-1}\right) = \frac{3}{2} \cdot (-1)x^{-1-1} = -\frac{3}{2}x^{-2}$$

This can also be written as $-\frac{3}{2x^2}$.

The derivative of the entire expression is the sum of the derivatives of its individual terms:

$$f'(x) = 9x^2 + 2 - \frac{3}{2x^2}$$

The derivation of the expression is:

$$9x^2 + 2 - \frac{3}{2x^2}$$