Solve 16y^2/9=

$$1 \frac { 6 y ^ { 2 } } { 9 } =$$

Evaluate

$$\frac{2y^{2}}{3}$$

Solution Steps

Divide 6y^{2} by 9 to get \frac{2}{3}y^{2}.

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

Multiply 1 and \frac{2}{3} to get \frac{2}{3}.

$$\frac{2}{3}y^{2}$$

Differentiate w.r.t. y

$$\frac{4y}{3}$$

Steps Using Definition of a Derivative

Divide 6y^{2} by 9 to get \frac{2}{3}y^{2}.

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

Multiply 1 and \frac{2}{3} to get \frac{2}{3}.

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

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

$$2\times \frac{2}{3}y^{2-1}$$

Multiply 2 times \frac{2}{3}.

$$\frac{4}{3}y^{2-1}$$

Subtract 1 from 2.

$$\frac{4}{3}y^{1}$$

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

$$\frac{4}{3}y$$