Solve d/dxleft(xleft(x-1right)^2right)

$$\frac{d}{d x } \left(x { \left(x-1 \right) }^{ 2 } \right)$$

Evaluate

$$\left(x-1\right)\left(3x-1\right)$$

Steps Using Derivative Rule for Sum

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\left(x^{2}-2x+1\right))$$

Use the distributive property to multiply x by x^{2}-2x+1.

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

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}.

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

Subtract 1 from 3.

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

Multiply 2 times -2.

$$3x^{2}-4x^{2-1}+x^{1-1}$$

Subtract 1 from 2.

$$3x^{2}-4x^{1}+x^{1-1}$$

Subtract 1 from 1.

$$3x^{2}-4x^{1}+x^{0}$$

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

$$3x^{2}-4x+x^{0}$$

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

$$3x^{2}-4x+1$$

Differentiate w.r.t. x

$$6x-4$$