Solve 6x^4-32x^3+24x+1

$$6 x ^ { 4 } - 32 x ^ { 3 } + 24 x + 1$$

Differentiate w.r.t. x

$$24\left(x^{3}-4x^{2}+1\right)$$

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}.

$$4\times 6x^{4-1}+3\left(-32\right)x^{3-1}+24x^{1-1}$$

Multiply 4 times 6.

$$24x^{4-1}+3\left(-32\right)x^{3-1}+24x^{1-1}$$

Subtract 1 from 4.

$$24x^{3}+3\left(-32\right)x^{3-1}+24x^{1-1}$$

Multiply 3 times -32.

$$24x^{3}-96x^{3-1}+24x^{1-1}$$

Subtract 1 from 3.

$$24x^{3}-96x^{2}+24x^{1-1}$$

Subtract 1 from 1.

$$24x^{3}-96x^{2}+24x^{0}$$

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

$$24x^{3}-96x^{2}+24\times 1$$

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

$$24x^{3}-96x^{2}+24$$

Evaluate

$$6x^{4}-32x^{3}+24x+1$$