Solve 7/21y1/3

$$\frac { 7 } { 21 } y \frac { 1 } { 3 }$$

Evaluate

$$\frac{y}{9}$$

Solution Steps

Reduce the fraction \frac{7}{21} to lowest terms by extracting and canceling out 7.

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

Multiply \frac{1}{3} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 1}{3\times 3}.

$$\frac{1}{9}y$$

Differentiate w.r.t. y

$$\frac{1}{9} = 0.1111111111111111$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{7}{21} to lowest terms by extracting and canceling out 7.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{3}y\times \frac{1}{3})$$

Multiply \frac{1}{3} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1\times 1}{3\times 3}y)$$

Do the multiplications in the fraction \frac{1\times 1}{3\times 3}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{9}y)$$

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

$$\frac{1}{9}y^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{9}y^{0}$$

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

$$\frac{1}{9}\times 1$$

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

$$\frac{1}{9}$$