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

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

Differentiate w.r.t. a

$$-20a^{4}-3$$

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}.

$$3\left(-4a^{2}\right)a^{3-1}-3a^{1-1}$$

Multiply 3 times -4a^{2}.

$$\left(-12a^{2}\right)a^{3-1}-3a^{1-1}$$

Subtract 1 from 3.

$$\left(-12a^{2}\right)a^{2}-3a^{1-1}$$

Subtract 1 from 1.

$$\left(-12a^{2}\right)a^{2}-3a^{0}$$

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

$$\left(-12a^{2}\right)a^{2}-3$$

Evaluate

$$2-3a-4a^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-4a^{5}-3a+2$$