Solve z^2*(-1)^2*3^2

$$z ^ { 2 } \cdot ( - 1 ) ^ { 2 } \cdot 3 ^ { 2 }$$

Evaluate

$$9z^{2}$$

Solution Steps

Calculate -1 to the power of 2 and get 1.

$$z^{2}\times 1\times 3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$z^{2}\times 1\times 9$$

Multiply 1 and 9 to get 9.

$$z^{2}\times 9$$

Differentiate w.r.t. z

$$18z$$

Steps Using Definition of a Derivative

Calculate -1 to the power of 2 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}z}(z^{2}\times 1\times 3^{2})$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\mathrm{d}}{\mathrm{d}z}(z^{2}\times 1\times 9)$$

Multiply 1 and 9 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}z}(z^{2}\times 9)$$

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

$$2\times 9z^{2-1}$$

Multiply 2 times 9.

$$18z^{2-1}$$

Subtract 1 from 2.

$$18z^{1}$$

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

$$18z$$