Solve 3x(x+2){(e)^x}

$$3x(x+2) {(e)^{ x }}$$

Differentiate w.r.t. x

$$3\left(x^{2}+4x+2\right)e^{x}$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(3x^{2}+6x\right)e^{x})$$

Use the distributive property to multiply 3x^{2}+6x by e^{x}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}e^{x}+6xe^{x})$$

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}.

$$2\times 3e^{x}x^{2-1}+6e^{x}x^{1-1}$$

Multiply 2 times 3e^{x}.

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

Subtract 1 from 2.

$$6e^{x}x^{1}+6e^{x}x^{1-1}$$

Subtract 1 from 1.

$$6e^{x}x^{1}+6e^{x}x^{0}$$

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

$$6e^{x}x+6e^{x}x^{0}$$

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

$$6e^{x}x+6e^{x}\times 1$$

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

$$6e^{x}x+6e^{x}$$

Evaluate

$$3x\left(x+2\right)e^{x}$$