What is application of derivatives in atual life

Question

If y=e^{log_e(log x)2}             

 

Fine    dy/dx . 

 

 

 

 

What is used of ??sum in atual life 

Answer 1

y = e^{ln(logx)^2}

 

The exponential and the natural log undo each other. So, you really have

 

y = (logx)²

 

This power of 2 is over the entire logx. It means log(x)*log(x). Do not get it confused with log(x²) = 2logx.

 

To find dy/dx, you need to use the chain rule.

 

dy/dx = 2(logx)*[1/x*ln(10)]

 

Derivatives are extremely important. They describe how things change. Most Physics and Engineering equations contain derivatives. Derivatives occur ubiquitously in Nature!