Solve (15x^2)^0(3z^3)

$$( 15 x ^ { 2 } ) ^ { 0 } ( 3 z ^ { 3 } )$$

Evaluate

$$3z^{3}$$

Solution Steps

Calculate 15x^{2} to the power of 0 and get 1.

$$1\times 3z^{3}$$

Multiply 1 and 3 to get 3.

$$3z^{3}$$

Differentiate w.r.t. z

$$9z^{2}$$

Steps Using Definition of a Derivative

Calculate 15x^{2} to the power of 0 and get 1.

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

Multiply 1 and 3 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}z}(3z^{3})$$

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

$$3\times 3z^{3-1}$$

Multiply 3 times 3.

$$9z^{3-1}$$

Subtract 1 from 3.

$$9z^{2}$$