Solve d/dx(2x^3-9x^2+12x-3)

$$\frac { d } { d x } ( 2 x ^ { 3 } - 9 x ^ { 2 } + 12 x - 3 )$$

Evaluate

$$6\left(x-2\right)\left(x-1\right)$$

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}.

$$3\times 2x^{3-1}+2\left(-9\right)x^{2-1}+12x^{1-1}$$

Multiply 3 times 2.

$$6x^{3-1}+2\left(-9\right)x^{2-1}+12x^{1-1}$$

Subtract 1 from 3.

$$6x^{2}+2\left(-9\right)x^{2-1}+12x^{1-1}$$

Multiply 2 times -9.

$$6x^{2}-18x^{2-1}+12x^{1-1}$$

Subtract 1 from 2.

$$6x^{2}-18x^{1}+12x^{1-1}$$

Subtract 1 from 1.

$$6x^{2}-18x^{1}+12x^{0}$$

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

$$6x^{2}-18x+12x^{0}$$

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

$$6x^{2}-18x+12\times 1$$

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

$$6x^{2}-18x+12$$

Differentiate w.r.t. x

$$12x-18$$