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Differentiate w.r.t. x
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\frac{6164646}{21096\sqrt{302}\times \frac{6361346}{3x\times \frac{3}{9}}}
Multiply 6 and 3516 to get 21096.
\frac{6164646}{21096\sqrt{302}\times \frac{6361346}{3x\times \frac{1}{3}}}
Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.
\frac{6164646}{21096\sqrt{302}\times \frac{6361346}{x}}
Cancel out 3 and 3.
\frac{6164646}{\frac{21096\times 6361346}{x}\sqrt{302}}
Express 21096\times \frac{6361346}{x} as a single fraction.
\frac{6164646\sqrt{302}}{\frac{21096\times 6361346}{x}\left(\sqrt{302}\right)^{2}}
Rationalize the denominator of \frac{6164646}{\frac{21096\times 6361346}{x}\sqrt{302}} by multiplying numerator and denominator by \sqrt{302}.
\frac{6164646\sqrt{302}}{\frac{21096\times 6361346}{x}\times 302}
The square of \sqrt{302} is 302.
\frac{6164646\sqrt{302}}{\frac{134198955216}{x}\times 302}
Multiply 21096 and 6361346 to get 134198955216.
\frac{6164646\sqrt{302}}{\frac{134198955216\times 302}{x}}
Express \frac{134198955216}{x}\times 302 as a single fraction.
\frac{6164646\sqrt{302}x}{134198955216\times 302}
Divide 6164646\sqrt{302} by \frac{134198955216\times 302}{x} by multiplying 6164646\sqrt{302} by the reciprocal of \frac{134198955216\times 302}{x}.
\frac{1027441\sqrt{302}x}{302\times 22366492536}
Cancel out 6 in both numerator and denominator.
\frac{1027441x}{22366492536\sqrt{302}}
Cancel out \sqrt{302} in both numerator and denominator.
\frac{1027441x\sqrt{302}}{22366492536\left(\sqrt{302}\right)^{2}}
Rationalize the denominator of \frac{1027441x}{22366492536\sqrt{302}} by multiplying numerator and denominator by \sqrt{302}.
\frac{1027441x\sqrt{302}}{22366492536\times 302}
The square of \sqrt{302} is 302.
\frac{1027441x\sqrt{302}}{6754680745872}
Multiply 22366492536 and 302 to get 6754680745872.