Solve 2-27-27m+27m^2-m^3

$$2 - 27 - 27 m + 27 m ^ { 2 } - m ^ { 3 }$$

Differentiate w.r.t. m

$$-3m^{2}+54m-27$$

Steps Using Derivative Rule for Sum

Subtract 27 from 2 to get -25.

$$\frac{\mathrm{d}}{\mathrm{d}m}(-25-27m+27m^{2}-m^{3})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-27m^{1-1}+2\times 27m^{2-1}+3\left(-1\right)m^{3-1}$$

Subtract 1 from 1.

$$-27m^{0}+2\times 27m^{2-1}+3\left(-1\right)m^{3-1}$$

Multiply 2 times 27.

$$-27m^{0}+54m^{2-1}+3\left(-1\right)m^{3-1}$$

Subtract 1 from 2.

$$-27m^{0}+54m^{1}+3\left(-1\right)m^{3-1}$$

Multiply 2 times 27.

$$-27m^{0}+54m^{1}-3m^{3-1}$$

Subtract 1 from 3.

$$-27m^{0}+54m^{1}-3m^{2}$$

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

$$-27m^{0}+54m-3m^{2}$$

For any term t except 0, t^{0}=1.

$$-27+54m-3m^{2}$$

Evaluate

$$-m^{3}+27m^{2}-27m-25$$

Solution Steps

Subtract 27 from 2 to get -25.

$$-25-27m+27m^{2}-m^{3}$$