Solve d/dxleft(xleft(30-2xright)^2right)

$$\frac{d}{d x } \left(x { \left(30-2x \right) }^{ 2 } \right)$$

Evaluate

$$12\left(x-15\right)\left(x-5\right)$$

Steps Using Derivative Rule for Sum

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(30-2x\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\left(900-120x+4x^{2}\right))$$

Use the distributive property to multiply x by 900-120x+4x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(900x-120x^{2}+4x^{3})$$

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}.

$$900x^{1-1}+2\left(-120\right)x^{2-1}+3\times 4x^{3-1}$$

Subtract 1 from 1.

$$900x^{0}+2\left(-120\right)x^{2-1}+3\times 4x^{3-1}$$

Multiply 2 times -120.

$$900x^{0}-240x^{2-1}+3\times 4x^{3-1}$$

Subtract 1 from 2.

$$900x^{0}-240x^{1}+3\times 4x^{3-1}$$

Multiply 2 times -120.

$$900x^{0}-240x^{1}+12x^{3-1}$$

Subtract 1 from 3.

$$900x^{0}-240x^{1}+12x^{2}$$

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

$$900x^{0}-240x+12x^{2}$$

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

$$900\times 1-240x+12x^{2}$$

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

$$900-240x+12x^{2}$$

Differentiate w.r.t. x

$$24\left(x-10\right)$$