Solve 42382600^2x/5225sqrt{5222}

$${ 42382600 }^{ 2 } \frac{ x }{ 5225 \sqrt{ 5222 } }$$

Evaluate

$$\frac{35925695655200\sqrt{5222}x}{545699}$$

Solution Steps

Calculate 42382600 to the power of 2 and get 1796284782760000.

$$1796284782760000\times \frac{x}{5225\sqrt{5222}}$$

Rationalize the denominator of \frac{x}{5225\sqrt{5222}} by multiplying numerator and denominator by \sqrt{5222}.

$$1796284782760000\times \frac{x\sqrt{5222}}{5225\left(\sqrt{5222}\right)^{2}}$$

The square of \sqrt{5222} is 5222.

$$1796284782760000\times \frac{x\sqrt{5222}}{5225\times 5222}$$

Multiply 5225 and 5222 to get 27284950.

$$1796284782760000\times \frac{x\sqrt{5222}}{27284950}$$

Express 1796284782760000\times \frac{x\sqrt{5222}}{27284950} as a single fraction.

$$\frac{1796284782760000x\sqrt{5222}}{27284950}$$

Divide 1796284782760000x\sqrt{5222} by 27284950 to get \frac{35925695655200}{545699}x\sqrt{5222}.

$$\frac{35925695655200}{545699}x\sqrt{5222}$$

Differentiate w.r.t. x

$$\frac{35925695655200 \sqrt{5222}}{545699} = 4757408697.955213$$