Solve 6x^4-7x^3+10x-23)div3x^2-2x+5

$$6 { x }^{ 4 } -7 { x }^{ 3 } +10x-23) \div 3 { x }^{ 2 } -2x+5$$

Differentiate w.r.t. x

$$24x^{3}-21x^{2}+10$$

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}.

$$4\times 6x^{4-1}+3\left(-7\right)x^{3-1}+10x^{1-1}$$

Multiply 4 times 6.

$$24x^{4-1}+3\left(-7\right)x^{3-1}+10x^{1-1}$$

Subtract 1 from 4.

$$24x^{3}+3\left(-7\right)x^{3-1}+10x^{1-1}$$

Multiply 3 times -7.

$$24x^{3}-21x^{3-1}+10x^{1-1}$$

Subtract 1 from 3.

$$24x^{3}-21x^{2}+10x^{1-1}$$

Subtract 1 from 1.

$$24x^{3}-21x^{2}+10x^{0}$$

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

$$24x^{3}-21x^{2}+10\times 1$$

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

$$24x^{3}-21x^{2}+10$$

Evaluate

$$6x^{4}-7x^{3}+10x-23$$