Solve -19a^3+12a^2+6a-7

$$- 19 a ^ { 3 } + 12 a ^ { 2 } + 6 a - 7$$

Differentiate w.r.t. a

$$6+24a-57a^{2}$$

Steps Using Derivative Rule for Sum

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}.

$$3\left(-19\right)a^{3-1}+2\times 12a^{2-1}+6a^{1-1}$$

Multiply 3 times -19.

$$-57a^{3-1}+2\times 12a^{2-1}+6a^{1-1}$$

Subtract 1 from 3.

$$-57a^{2}+2\times 12a^{2-1}+6a^{1-1}$$

Multiply 2 times 12.

$$-57a^{2}+24a^{2-1}+6a^{1-1}$$

Subtract 1 from 2.

$$-57a^{2}+24a^{1}+6a^{1-1}$$

Subtract 1 from 1.

$$-57a^{2}+24a^{1}+6a^{0}$$

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

$$-57a^{2}+24a+6a^{0}$$

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

$$-57a^{2}+24a+6\times 1$$

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

$$-57a^{2}+24a+6$$

Evaluate

$$-19a^{3}+12a^{2}+6a-7$$