Solve =2/3g^4-1-2

$$= \frac { 2 } { 3 } g ^ { 4 - 1 - 2 }$$

Evaluate

$$\frac{2g}{3}$$

Solution Steps

Subtract 1 from 4 to get 3.

$$\frac{2}{3}g^{3-2}$$

Subtract 2 from 3 to get 1.

$$\frac{2}{3}g^{1}$$

Calculate g to the power of 1 and get g.

$$\frac{2}{3}g$$

Differentiate w.r.t. g

$$\frac{2}{3} = 0.6666666666666666$$

Steps Using Definition of a Derivative

Subtract 1 from 4 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{2}{3}g^{3-2})$$

Subtract 2 from 3 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{2}{3}g^{1})$$

Calculate g to the power of 1 and get g.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{2}{3}g)$$

The derivative of ax^{n} is nax^{n-1}.

$$\frac{2}{3}g^{1-1}$$

Subtract 1 from 1.

$$\frac{2}{3}g^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{2}{3}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{2}{3}$$