Solve (5x-x^3+2x-1)+(x^3-5x)

$$( 5 x - x ^ { 3 } + 2 x - 1 ) + ( x ^ { 3 } - 5 x )$$

Evaluate

$$2x-1$$

Solution Steps

Combine 5x and 2x to get 7x.

$$7x-x^{3}-1+x^{3}-5x$$

Combine -x^{3} and x^{3} to get 0.

$$7x-1-5x$$

Combine 7x and -5x to get 2x.

$$2x-1$$

Differentiate w.r.t. x

$$2$$

Steps Using Derivative Rule for Sum

Combine 5x and 2x to get 7x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x-x^{3}-1+x^{3}-5x)$$

Combine -x^{3} and x^{3} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x-1-5x)$$

Combine 7x and -5x to get 2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x-1)$$

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}.

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

Subtract 1 from 1.

$$2x^{0}$$

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

$$2\times 1$$

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

$$2$$