Solve (2x)(2x)-3x+6=

$$( 2 x ) ( 2 x ) - 3 x + 6 =$$

Evaluate

$$4x^{2}-3x+6$$

Solution Steps

Multiply x and x to get x^{2}.

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

Multiply 2 and 2 to get 4.

$$4x^{2}-3x+6$$

Differentiate w.r.t. x

$$8x-3$$

Steps Using Derivative Rule for Sum

Multiply x and x to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}\times 2-3x+6)$$

Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{2}-3x+6)$$

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}.

$$2\times 4x^{2-1}-3x^{1-1}$$

Multiply 2 times 4.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

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

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

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

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

$$8x-3$$