Solve frac{sqrt{3}}{(5)-x^4*(-x)^3}

$$\frac { \sqrt { 3 } } { ( 5 ) - x ^ { 4 } \times ( - x ) ^ { 3 } }$$

Evaluate

$$\frac{\sqrt{3}}{x^{7}+5}$$

Solution Steps

Expand \left(-x\right)^{3}.

$$\frac{\sqrt{3}}{5-x^{4}\left(-1\right)^{3}x^{3}}$$

Calculate -1 to the power of 3 and get -1.

$$\frac{\sqrt{3}}{5-x^{4}\left(-1\right)x^{3}}$$

Multiply -1 and -1 to get 1.

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

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{\sqrt{3}}{5+x^{7}}$$

Differentiate w.r.t. x

$$-\frac{7\sqrt{3}x^{6}}{\left(x^{7}+5\right)^{2}}$$