Solve =0.31y*1/2

$$= 0.31 y \times \frac { 1 } { 2 }$$

Evaluate

$$\frac{31y}{200}$$

Solution Steps

Convert decimal number 0.31 to fraction \frac{31}{100}.

$$\frac{31}{100}y\times \frac{1}{2}$$

Multiply \frac{31}{100} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{31\times 1}{100\times 2}y$$

Do the multiplications in the fraction \frac{31\times 1}{100\times 2}.

$$\frac{31}{200}y$$

Differentiate w.r.t. y

$$0.155$$

Steps Using Definition of a Derivative

Convert decimal number 0.31 to fraction \frac{31}{100}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{31}{100}y\times \frac{1}{2})$$

Multiply \frac{31}{100} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{31\times 1}{100\times 2}y)$$

Do the multiplications in the fraction \frac{31\times 1}{100\times 2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{31}{200}y)$$

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

$$\frac{31}{200}y^{1-1}$$

Subtract 1 from 1.

$$\frac{31}{200}y^{0}$$

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

$$\frac{31}{200}\times 1$$

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

$$\frac{31}{200}$$