Solve d/dxleft(left(3x-1right)^2(1-4x)right)

$$\frac{d}{d x } \left( { \left(3x-1 \right) }^{ 2 } (1-4x) \right)$$

Evaluate

$$-108x^{2}+66x-10$$

Steps Using Derivative Rule for Sum

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-1\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(9x^{2}-6x+1\right)\left(1-4x\right))$$

Use the distributive property to multiply 9x^{2}-6x+1 by 1-4x and combine like terms.

$$\frac{\mathrm{d}}{\mathrm{d}x}(33x^{2}-36x^{3}-10x+1)$$

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}.

$$2\times 33x^{2-1}+3\left(-36\right)x^{3-1}-10x^{1-1}$$

Multiply 2 times 33.

$$66x^{2-1}+3\left(-36\right)x^{3-1}-10x^{1-1}$$

Subtract 1 from 2.

$$66x^{1}+3\left(-36\right)x^{3-1}-10x^{1-1}$$

Multiply 3 times -36.

$$66x^{1}-108x^{3-1}-10x^{1-1}$$

Subtract 1 from 3.

$$66x^{1}-108x^{2}-10x^{1-1}$$

Subtract 1 from 1.

$$66x^{1}-108x^{2}-10x^{0}$$

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

$$66x-108x^{2}-10x^{0}$$

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

$$66x-108x^{2}-10$$

Differentiate w.r.t. x

$$66-216x$$