Solve (6x^3-2x^2+9x-8)+(4x^3-2x+6)

$$( 6 x ^ { 3 } - 2 x ^ { 2 } + 9 x - 8 ) + ( 4 x ^ { 3 } - 2 x + 6 )$$

Evaluate

$$10x^{3}-2x^{2}+7x-2$$

Solution Steps

Combine 6x^{3} and 4x^{3} to get 10x^{3}.

$$10x^{3}-2x^{2}+9x-8-2x+6$$

Combine 9x and -2x to get 7x.

$$10x^{3}-2x^{2}+7x-8+6$$

Add -8 and 6 to get -2.

$$10x^{3}-2x^{2}+7x-2$$

Differentiate w.r.t. x

$$30x^{2}-4x+7$$

Steps Using Derivative Rule for Sum

Combine 6x^{3} and 4x^{3} to get 10x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{3}-2x^{2}+9x-8-2x+6)$$

Combine 9x and -2x to get 7x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{3}-2x^{2}+7x-8+6)$$

Add -8 and 6 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{3}-2x^{2}+7x-2)$$

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}.

$$3\times 10x^{3-1}+2\left(-2\right)x^{2-1}+7x^{1-1}$$

Multiply 3 times 10.

$$30x^{3-1}+2\left(-2\right)x^{2-1}+7x^{1-1}$$

Subtract 1 from 3.

$$30x^{2}+2\left(-2\right)x^{2-1}+7x^{1-1}$$

Multiply 2 times -2.

$$30x^{2}-4x^{2-1}+7x^{1-1}$$

Subtract 1 from 2.

$$30x^{2}-4x^{1}+7x^{1-1}$$

Subtract 1 from 1.

$$30x^{2}-4x^{1}+7x^{0}$$

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

$$30x^{2}-4x+7x^{0}$$

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

$$30x^{2}-4x+7\times 1$$

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

$$30x^{2}-4x+7$$