Solve 09x^8-100y^2

$$09 x ^ { 8 } - 100 y ^ { 2 }$$

Evaluate

$$-100y^{2}$$

Solution Steps

Multiply 0 and 9 to get 0.

$$0x^{8}-100y^{2}$$

Anything times zero gives zero.

$$0-100y^{2}$$

Anything plus zero gives itself.

$$-100y^{2}$$

Differentiate w.r.t. y

$$-200y$$

Steps Using Definition of a Derivative

Multiply 0 and 9 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}y}(0x^{8}-100y^{2})$$

Anything times zero gives zero.

$$\frac{\mathrm{d}}{\mathrm{d}y}(0-100y^{2})$$

Anything plus zero gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-100y^{2})$$

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

$$2\left(-100\right)y^{2-1}$$

Multiply 2 times -100.

$$-200y^{2-1}$$

Subtract 1 from 2.

$$-200y^{1}$$

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

$$-200y$$