Solve x^3+2xx^3+8

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

Differentiate w.r.t. x

$$\left(8x+3\right)x^{2}$$

Steps Using Derivative Rule for Sum

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}.

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

Subtract 1 from 3.

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

Subtract 1 from 1.

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

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

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

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

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

Evaluate

$$2x^{4}+x^{3}+8$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$x^{3}+2x^{4}+8$$