Solve (7x^3-2)+(5x^3-x-3)

$$(7 { x }^{ 3 } -2)+(5 { x }^{ 3 } -x-3)$$

Evaluate

$$12x^{3}-x-5$$

Solution Steps

Combine 7x^{3} and 5x^{3} to get 12x^{3}.

$$12x^{3}-2-x-3$$

Subtract 3 from -2 to get -5.

$$12x^{3}-5-x$$

Differentiate w.r.t. x

$$36x^{2}-1$$

Steps Using Derivative Rule for Sum

Combine 7x^{3} and 5x^{3} to get 12x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{3}-2-x-3)$$

Subtract 3 from -2 to get -5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{3}-5-x)$$

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}.

$$3\times 12x^{3-1}-x^{1-1}$$

Multiply 3 times 12.

$$36x^{3-1}-x^{1-1}$$

Subtract 1 from 3.

$$36x^{2}-x^{1-1}$$

Subtract 1 from 1.

$$36x^{2}-x^{0}$$

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

$$36x^{2}-1$$