Solve (7-3x)+(3x^2+2x+8)

$$( 7 - 3 x ) + ( 3 x ^ { 2 } + 2 x + 8 )$$

Evaluate

$$3x^{2}-x+15$$

Solution Steps

Combine -3x and 2x to get -x.

$$7-x+3x^{2}+8$$

Add 7 and 8 to get 15.

$$15-x+3x^{2}$$

Differentiate w.r.t. x

$$6x-1$$

Steps Using Derivative Rule for Sum

Combine -3x and 2x to get -x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7-x+3x^{2}+8)$$

Add 7 and 8 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15-x+3x^{2})$$

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}.

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

Subtract 1 from 1.

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

Multiply 2 times 3.

$$-x^{0}+6x^{2-1}$$

Subtract 1 from 2.

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

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

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

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

$$-1+6x$$