Solve 2^3x^0y^5

$$2 ^ { 3 } x ^ { 0 } y ^ { 5 }$$

Evaluate

$$8y^{5}$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$8x^{0}y^{5}$$

Calculate x to the power of 0 and get 1.

$$8\times 1y^{5}$$

Multiply 8 and 1 to get 8.

$$8y^{5}$$

Differentiate w.r.t. y

$$40y^{4}$$

Steps Using Definition of a Derivative

Calculate 2 to the power of 3 and get 8.

$$\frac{\mathrm{d}}{\mathrm{d}y}(8x^{0}y^{5})$$

Calculate x to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}y}(8\times 1y^{5})$$

Multiply 8 and 1 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}y}(8y^{5})$$

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

$$5\times 8y^{5-1}$$

Multiply 5 times 8.

$$40y^{5-1}$$

Subtract 1 from 5.

$$40y^{4}$$