Solve 4m-3+4m^2+7-9m

$$4 m - 3 + 4 m ^ { 2 } + 7 - 9 m$$

Evaluate

$$4m^{2}-5m+4$$

Solution Steps

Add -3 and 7 to get 4.

$$4m+4+4m^{2}-9m$$

Combine 4m and -9m to get -5m.

$$-5m+4+4m^{2}$$

Differentiate w.r.t. m

$$8m-5$$

Steps Using Derivative Rule for Sum

Add -3 and 7 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}m}(4m+4+4m^{2}-9m)$$

Combine 4m and -9m to get -5m.

$$\frac{\mathrm{d}}{\mathrm{d}m}(-5m+4+4m^{2})$$

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}.

$$-5m^{1-1}+2\times 4m^{2-1}$$

Subtract 1 from 1.

$$-5m^{0}+2\times 4m^{2-1}$$

Multiply 2 times 4.

$$-5m^{0}+8m^{2-1}$$

Subtract 1 from 2.

$$-5m^{0}+8m^{1}$$

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

$$-5m^{0}+8m$$

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

$$-5+8m$$