Solve 3x^2-2x+6+2x^2+x+1=

$$3 x ^ { 2 } - 2 x + 6 + 2 x ^ { 2 } + x + 1 =$$

Evaluate

$$5x^{2}-x+7$$

Solution Steps

Combine 3x^{2} and 2x^{2} to get 5x^{2}.

$$5x^{2}-2x+6+x+1$$

Combine -2x and x to get -x.

$$5x^{2}-x+6+1$$

Add 6 and 1 to get 7.

$$5x^{2}-x+7$$

Differentiate w.r.t. x

$$10x-1$$

Steps Using Derivative Rule for Sum

Combine 3x^{2} and 2x^{2} to get 5x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{2}-2x+6+x+1)$$

Combine -2x and x to get -x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{2}-x+6+1)$$

Add 6 and 1 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{2}-x+7)$$

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}.

$$2\times 5x^{2-1}-x^{1-1}$$

Multiply 2 times 5.

$$10x^{2-1}-x^{1-1}$$

Subtract 1 from 2.

$$10x^{1}-x^{1-1}$$

Subtract 1 from 1.

$$10x^{1}-x^{0}$$

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

$$10x-x^{0}$$

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

$$10x-1$$