Solve -10a^3+6a^2-4a+3

$$- 10 a ^ { 3 } + 6 a ^ { 2 } - 4 a + 3$$

Differentiate w.r.t. a

$$-30a^{2}+12a-4$$

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}.

$$3\left(-10\right)a^{3-1}+2\times 6a^{2-1}-4a^{1-1}$$

Multiply 3 times -10.

$$-30a^{3-1}+2\times 6a^{2-1}-4a^{1-1}$$

Subtract 1 from 3.

$$-30a^{2}+2\times 6a^{2-1}-4a^{1-1}$$

Multiply 2 times 6.

$$-30a^{2}+12a^{2-1}-4a^{1-1}$$

Subtract 1 from 2.

$$-30a^{2}+12a^{1}-4a^{1-1}$$

Subtract 1 from 1.

$$-30a^{2}+12a^{1}-4a^{0}$$

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

$$-30a^{2}+12a-4a^{0}$$

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

$$-30a^{2}+12a-4$$

Evaluate

$$3-4a+6a^{2}-10a^{3}$$