Solve (3(x+1)x^2)^prime

$$( 3 ( x + 1 ) x ^ { 2 } ) ^ { \prime }$$

Evaluate

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

Steps Using Derivative Rule for Sum

Use the distributive property to multiply 3 by x+1.

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

Use the distributive property to multiply 3x+3 by x^{2}.

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

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}.

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

Multiply 3 times 3.

$$9x^{3-1}+2\times 3x^{2-1}$$

Subtract 1 from 3.

$$9x^{2}+2\times 3x^{2-1}$$

Multiply 2 times 3.

$$9x^{2}+6x^{2-1}$$

Subtract 1 from 2.

$$9x^{2}+6x^{1}$$

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

$$9x^{2}+6x$$

Differentiate w.r.t. x

$$18x+6$$