Solve x^3sqrt{3}(x^2sqrt{3}+x+3sqrt{3})

$$x ^ { 3 } \sqrt { 3 } ( x ^ { 2 } \sqrt { 3 } + x + 3 \sqrt { 3 } )$$

Evaluate

$$3x^{5}+\sqrt{3}x^{4}+9x^{3}$$

Solution Steps

Use the distributive property to multiply x^{3}\sqrt{3} by x^{2}\sqrt{3}+x+3\sqrt{3}.

$$x^{5}\left(\sqrt{3}\right)^{2}+\sqrt{3}x^{4}+3x^{3}\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$x^{5}\times 3+\sqrt{3}x^{4}+3x^{3}\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$x^{5}\times 3+\sqrt{3}x^{4}+3x^{3}\times 3$$

Multiply 3 and 3 to get 9.

$$x^{5}\times 3+\sqrt{3}x^{4}+9x^{3}$$

Differentiate w.r.t. x

$$x^{2}\left(15x^{2}+4\sqrt{3}x+27\right)$$