Solve (mm)quad(a^-3b^-3)^0

$$( m m ) \quad ( a ^ { - 3 } b ^ { - 3 } ) ^ { 0 }$$

Evaluate

$$m^{2}$$

Solution Steps

Multiply m and m to get m^{2}.

$$m^{2}\left(a^{-3}b^{-3}\right)^{0}$$

Calculate a^{-3}b^{-3} to the power of 0 and get 1.

$$m^{2}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$m^{2}$$

Differentiate w.r.t. m

$$2m$$

Steps Using Definition of a Derivative

Multiply m and m to get m^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{2}\left(a^{-3}b^{-3}\right)^{0})$$

Calculate a^{-3}b^{-3} to the power of 0 and get 1.

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

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

$$2m^{2-1}$$

Subtract 1 from 2.

$$2m^{1}$$

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

$$2m$$