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

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

Evaluate

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

Steps Using Chain Rule

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

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

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}.

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

Simplify.

$$2x^{0}\left(x^{1}-1\right)^{1}$$

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

$$2x^{0}\left(x-1\right)$$

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

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

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

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

Differentiate w.r.t. x

$$2$$