On March 30th, we started off the class by doing some review problems. The review problems involved the derivatives of logs and natural logs. They also included the derivative of of e. Next we found a way to derive something such as y= log base10 of x. We changed this to 10^y=x. We then used natural logs to make it yln10=lnx. y=lnx/ln10. We then took the derivative of this which was 1/ln10*1/x. We used this derivative to find other derivatives of log functions.We then used the same rules to find the derivatives of exponential functions and also a function where there is a variable in the base and a variable in the exponent. The derivative of x^lnx is (x^lnx*2lnx)/x. The derivative of 2^-x^2+1 is 2^-x^2+1*-2x*ln2. Implicit differentiation can be used while finding these derivatives. We found out how to find the derivative for three different kinds of equations today.
On April 1st, we began class by reviewing the reading assigned for homework. We discussed that, at times, even when a graph has a positive and negative slope, only the positive slope can be take into consideration if the equation for the derivative is something like 2/the square root of y. This is because the square root of y must be positive. We also said that is the derivative equaiton is something -xy/ln y and the first original equation is y=e ^(the square root of 4-x^2), the domain should not include where x makes the equation equal zero because you would end up dividing by 0. Next, we reviewed slope fields. We learned how to sketch solution curves and to create equations for tangent lines as well as find particular solutions for equations with initial conditions and how to find their domain.
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On March 30th, we started off the class by doing some review problems. The review problems involved the derivatives of logs and natural logs. They also included the derivative of of e. Next we found a way to derive something such as y= log base10 of x. We changed this to 10^y=x. We then used natural logs to make it yln10=lnx. y=lnx/ln10. We then took the derivative of this which was 1/ln10*1/x. We used this derivative to find other derivatives of log functions.We then used the same rules to find the derivatives of exponential functions and also a function where there is a variable in the base and a variable in the exponent. The derivative of x^lnx is (x^lnx*2lnx)/x. The derivative of 2^-x^2+1 is 2^-x^2+1*-2x*ln2. Implicit differentiation can be used while finding these derivatives. We found out how to find the derivative for three different kinds of equations today.
On April 1st, we began class by reviewing the reading assigned for homework. We discussed that, at times, even when a graph has a positive and negative slope, only the positive slope can be take into consideration if the equation for the derivative is something like 2/the square root of y. This is because the square root of y must be positive. We also said that is the derivative equaiton is something -xy/ln y and the first original equation is y=e ^(the square root of 4-x^2), the domain should not include where x makes the equation equal zero because you would end up dividing by 0. Next, we reviewed slope fields. We learned how to sketch solution curves and to create equations for tangent lines as well as find particular solutions for equations with initial conditions and how to find their domain.
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