Solve d/dx[3(2x^2)*(-4x+8)^2]

$$\frac { d } { d x } [ 3 ( 2 x ^ { 2 } ) \cdot ( - 4 x + 8 ) ^ { 2 } ]$$

Evaluate

$$384x\left(x-2\right)\left(x-1\right)$$

Steps Using Derivative Rule for Sum

Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{2}\left(-4x+8\right)^{2})$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-4x+8\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{2}\left(16x^{2}-64x+64\right))$$

Use the distributive property to multiply 6x^{2} by 16x^{2}-64x+64.

$$\frac{\mathrm{d}}{\mathrm{d}x}(96x^{4}-384x^{3}+384x^{2})$$

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}.

$$4\times 96x^{4-1}+3\left(-384\right)x^{3-1}+2\times 384x^{2-1}$$

Multiply 4 times 96.

$$384x^{4-1}+3\left(-384\right)x^{3-1}+2\times 384x^{2-1}$$

Subtract 1 from 4.

$$384x^{3}+3\left(-384\right)x^{3-1}+2\times 384x^{2-1}$$

Multiply 3 times -384.

$$384x^{3}-1152x^{3-1}+2\times 384x^{2-1}$$

Subtract 1 from 3.

$$384x^{3}-1152x^{2}+2\times 384x^{2-1}$$

Multiply 3 times -384.

$$384x^{3}-1152x^{2}+768x^{2-1}$$

Subtract 1 from 2.

$$384x^{3}-1152x^{2}+768x^{1}$$

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

$$384x^{3}-1152x^{2}+768x$$

Differentiate w.r.t. x

$$1152x^{2}-2304x+768$$