Solve 8x^3+5+7x^2+6x?

$$8 x ^ { 3 } + 5 + 7 x ^ { 2 } + 6 x ?$$

Differentiate w.r.t. x

$$24x^{2}+14x+6$$

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}.

$$3\times 8x^{3-1}+2\times 7x^{2-1}+6x^{1-1}$$

Multiply 3 times 8.

$$24x^{3-1}+2\times 7x^{2-1}+6x^{1-1}$$

Subtract 1 from 3.

$$24x^{2}+2\times 7x^{2-1}+6x^{1-1}$$

Multiply 2 times 7.

$$24x^{2}+14x^{2-1}+6x^{1-1}$$

Subtract 1 from 2.

$$24x^{2}+14x^{1}+6x^{1-1}$$

Subtract 1 from 1.

$$24x^{2}+14x^{1}+6x^{0}$$

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

$$24x^{2}+14x+6x^{0}$$

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

$$24x^{2}+14x+6\times 1$$

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

$$24x^{2}+14x+6$$

Evaluate

$$8x^{3}+7x^{2}+6x+5$$