Solve d(3/2(1+x)^2)/dx

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

Evaluate

$$3\left(x+1\right)$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{2}\left(1+2x+x^{2}\right))$$

Use the distributive property to multiply \frac{3}{2} by 1+2x+x^{2}.

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

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}.

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

Subtract 1 from 1.

$$3x^{0}+2\times \frac{3}{2}x^{2-1}$$

Multiply 2 times \frac{3}{2}.

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

Subtract 1 from 2.

$$3x^{0}+3x^{1}$$

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

$$3x^{0}+3x$$

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

$$3\times 1+3x$$

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

$$3+3x$$

Differentiate w.r.t. x

$$3$$