Solve 3alpha1*5/80=

$$\frac { 3 \alpha 1 \cdot 5 } { 80 } =$$

Evaluate

$$\frac{3\alpha _{1}}{16}$$

Solution Steps

Multiply 3 and 5 to get 15.

$$\frac{15\alpha _{1}}{80}$$

Divide 15\alpha _{1} by 80 to get \frac{3}{16}\alpha _{1}.

$$\frac{3}{16}\alpha _{1}$$

Differentiate w.r.t. α_1

$$\frac{3}{16} = 0.1875$$

Steps Using Definition of a Derivative

Multiply 3 and 5 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}\alpha _{1}}(\frac{15\alpha _{1}}{80})$$

Divide 15\alpha _{1} by 80 to get \frac{3}{16}\alpha _{1}.

$$\frac{\mathrm{d}}{\mathrm{d}\alpha _{1}}(\frac{3}{16}\alpha _{1})$$

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

$$\frac{3}{16}\alpha _{1}^{1-1}$$

Subtract 1 from 1.

$$\frac{3}{16}\alpha _{1}^{0}$$

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

$$\frac{3}{16}\times 1$$

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

$$\frac{3}{16}$$