Solve {c}{8x^3-27-36x^2}{-54x}

$$\left. \begin{array} { c } { 8 x ^ { 3 } - 27 - 36 x ^ { 2 } } \\ { - 54 x } \end{array} \right.$$

Differentiate w.r.t. x

$$24x^{2}-72x-54$$

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}.

$$3\times 8x^{3-1}+2\left(-36\right)x^{2-1}-54x^{1-1}$$

Multiply 3 times 8.

$$24x^{3-1}+2\left(-36\right)x^{2-1}-54x^{1-1}$$

Subtract 1 from 3.

$$24x^{2}+2\left(-36\right)x^{2-1}-54x^{1-1}$$

Multiply 2 times -36.

$$24x^{2}-72x^{2-1}-54x^{1-1}$$

Subtract 1 from 2.

$$24x^{2}-72x^{1}-54x^{1-1}$$

Subtract 1 from 1.

$$24x^{2}-72x^{1}-54x^{0}$$

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

$$24x^{2}-72x-54x^{0}$$

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

$$24x^{2}-72x-54$$

Evaluate

$$8x^{3}-36x^{2}-54x-27$$