Solve 009x^2-1/4y^2

$$009 x ^ { 2 } - \frac { 1 } { 4 } y ^ { 2 }$$

Evaluate

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

Solution Steps

Multiply 0 and 0 to get 0.

$$0\times 9x^{2}-\frac{1}{4}y^{2}$$

Multiply 0 and 9 to get 0.

$$0x^{2}-\frac{1}{4}y^{2}$$

Anything times zero gives zero.

$$0-\frac{1}{4}y^{2}$$

Anything plus zero gives itself.

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

Differentiate w.r.t. y

$$-\frac{y}{2}$$

Steps Using Definition of a Derivative

Multiply 0 and 0 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}y}(0\times 9x^{2}-\frac{1}{4}y^{2})$$

Multiply 0 and 9 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}y}(0x^{2}-\frac{1}{4}y^{2})$$

Anything times zero gives zero.

$$\frac{\mathrm{d}}{\mathrm{d}y}(0-\frac{1}{4}y^{2})$$

Anything plus zero gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-\frac{1}{4}y^{2})$$

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

$$2\left(-\frac{1}{4}\right)y^{2-1}$$

Multiply 2 times -\frac{1}{4}.

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

Subtract 1 from 2.

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

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

$$-\frac{1}{2}y$$