Solve m^2-4m+3m^3-10m+100=

$$m ^ { 2 } - 4 m + 3 m ^ { 3 } - 10 m + 100 =$$

Differentiate w.r.t. m

$$9m^{2}+2m-14$$

Steps Using Derivative Rule for Sum

Combine -4m and -10m to get -14m.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{2}-14m+3m^{3}+100)$$

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}.

$$2m^{2-1}-14m^{1-1}+3\times 3m^{3-1}$$

Subtract 1 from 2.

$$2m^{1}-14m^{1-1}+3\times 3m^{3-1}$$

Subtract 1 from 1.

$$2m^{1}-14m^{0}+3\times 3m^{3-1}$$

Multiply 1 times -14.

$$2m^{1}-14m^{0}+9m^{3-1}$$

Subtract 1 from 3.

$$2m^{1}-14m^{0}+9m^{2}$$

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

$$2m-14m^{0}+9m^{2}$$

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

$$2m-14+9m^{2}$$

Evaluate

$$3m^{3}+m^{2}-14m+100$$

Solution Steps

Combine -4m and -10m to get -14m.

$$m^{2}-14m+3m^{3}+100$$