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

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

Evaluate

$$\left(x-2\right)\left(3x+4\right)$$

Steps Using Derivative Rule for Sum

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

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

Use the distributive property to multiply x^{2}-4x+4 by x+3 and combine like terms.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}-x^{2}-8x+12)$$

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}.

$$3x^{3-1}+2\left(-1\right)x^{2-1}-8x^{1-1}$$

Subtract 1 from 3.

$$3x^{2}+2\left(-1\right)x^{2-1}-8x^{1-1}$$

Multiply 2 times -1.

$$3x^{2}-2x^{2-1}-8x^{1-1}$$

Subtract 1 from 2.

$$3x^{2}-2x^{1}-8x^{1-1}$$

Subtract 1 from 1.

$$3x^{2}-2x^{1}-8x^{0}$$

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

$$3x^{2}-2x-8x^{0}$$

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

$$3x^{2}-2x-8$$

Differentiate w.r.t. x

$$6x-2$$