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

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

Differentiate w.r.t. x

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

Steps Using Derivative Rule for Sum

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

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

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}.

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

Subtract 1 from 3.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

$$3x^{2}+2x^{1}+2x^{0}$$

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

$$3x^{2}+2x+2x^{0}$$

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

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

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

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

Evaluate

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

Solution Steps

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

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