Solve 6a^3-8a^2-6a+57

$$6 a ^ { 3 } - 8 a ^ { 2 } - 6 a + 57$$

Differentiate w.r.t. a

$$18a^{2}-16a-6$$

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}.

$$3\times 6a^{3-1}+2\left(-8\right)a^{2-1}-6a^{1-1}$$

Multiply 3 times 6.

$$18a^{3-1}+2\left(-8\right)a^{2-1}-6a^{1-1}$$

Subtract 1 from 3.

$$18a^{2}+2\left(-8\right)a^{2-1}-6a^{1-1}$$

Multiply 2 times -8.

$$18a^{2}-16a^{2-1}-6a^{1-1}$$

Subtract 1 from 2.

$$18a^{2}-16a^{1}-6a^{1-1}$$

Subtract 1 from 1.

$$18a^{2}-16a^{1}-6a^{0}$$

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

$$18a^{2}-16a-6a^{0}$$

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

$$18a^{2}-16a-6$$

Evaluate

$$6a^{3}-8a^{2}-6a+57$$