Solve 009x^8-100y^4

$$009 x ^ { 8 } - 100 y ^ { 4 }$$

Evaluate

$$-100y^{4}$$

Solution Steps

Multiply 0 and 0 to get 0.

$$0\times 9x^{8}-100y^{4}$$

Multiply 0 and 9 to get 0.

$$0x^{8}-100y^{4}$$

Anything times zero gives zero.

$$0-100y^{4}$$

Anything plus zero gives itself.

$$-100y^{4}$$

Differentiate w.r.t. y

$$-400y^{3}$$

Steps Using Definition of a Derivative

Multiply 0 and 0 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}y}(0\times 9x^{8}-100y^{4})$$

Multiply 0 and 9 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}y}(0x^{8}-100y^{4})$$

Anything times zero gives zero.

$$\frac{\mathrm{d}}{\mathrm{d}y}(0-100y^{4})$$

Anything plus zero gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-100y^{4})$$

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

$$4\left(-100\right)y^{4-1}$$

Multiply 4 times -100.

$$-400y^{4-1}$$

Subtract 1 from 4.

$$-400y^{3}$$