Solve d/dx(x-1)(x-2)(x-3)

$$\frac { d } { d x } ( x - 1 ) ( x - 2 ) ( x - 3 )$$

Evaluate

$$3x^{2}-12x+11$$

Steps Using Derivative Rule for Sum

Apply the distributive property by multiplying each term of x-1 by each term of x-2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x^{2}-2x-x+2\right)\left(x-3\right))$$

Combine -2x and -x to get -3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x^{2}-3x+2\right)\left(x-3\right))$$

Apply the distributive property by multiplying each term of x^{2}-3x+2 by each term of x-3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}-3x^{2}-3x^{2}+9x+2x-6)$$

Combine -3x^{2} and -3x^{2} to get -6x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}-6x^{2}+9x+2x-6)$$

Combine 9x and 2x to get 11x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}-6x^{2}+11x-6)$$

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}.

$$3x^{3-1}+2\left(-6\right)x^{2-1}+11x^{1-1}$$

Subtract 1 from 3.

$$3x^{2}+2\left(-6\right)x^{2-1}+11x^{1-1}$$

Multiply 2 times -6.

$$3x^{2}-12x^{2-1}+11x^{1-1}$$

Subtract 1 from 2.

$$3x^{2}-12x^{1}+11x^{1-1}$$

Subtract 1 from 1.

$$3x^{2}-12x^{1}+11x^{0}$$

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

$$3x^{2}-12x+11x^{0}$$

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

$$3x^{2}-12x+11\times 1$$

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

$$3x^{2}-12x+11$$

Differentiate w.r.t. x

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