Solve frac{xsqrt{23511}}{{left(84122585xsqrt{952452}right)}^2}

$$\frac{ x \sqrt{ 23511 } }{ { \left(84122585x \sqrt{ 952452 } \right) }^{ 2 } }$$

Evaluate

$$\frac{\sqrt{23511}}{6740130687749079365700x}$$

Solution Steps

Factor 952452=6^{2}\times 26457. Rewrite the square root of the product \sqrt{6^{2}\times 26457} as the product of square roots \sqrt{6^{2}}\sqrt{26457}. Take the square root of 6^{2}.

$$\frac{x\sqrt{23511}}{\left(84122585x\times 6\sqrt{26457}\right)^{2}}$$

Multiply 84122585 and 6 to get 504735510.

$$\frac{x\sqrt{23511}}{\left(504735510x\sqrt{26457}\right)^{2}}$$

Expand \left(504735510x\sqrt{26457}\right)^{2}.

$$\frac{x\sqrt{23511}}{504735510^{2}x^{2}\left(\sqrt{26457}\right)^{2}}$$

Calculate 504735510 to the power of 2 and get 254757935054960100.

$$\frac{x\sqrt{23511}}{254757935054960100x^{2}\left(\sqrt{26457}\right)^{2}}$$

The square of \sqrt{26457} is 26457.

$$\frac{x\sqrt{23511}}{254757935054960100x^{2}\times 26457}$$

Multiply 254757935054960100 and 26457 to get 6740130687749079365700.

$$\frac{x\sqrt{23511}}{6740130687749079365700x^{2}}$$

Cancel out x in both numerator and denominator.

$$\frac{\sqrt{23511}}{6740130687749079365700x}$$

Differentiate w.r.t. x

$$-\frac{\sqrt{23511}}{6740130687749079365700x^{2}}$$