Category: Differential Calculus, Algebra
"Published in Vacaville, California, USA"
Given the following functions:
Find dy/dx.
Solution:
The first thing that we need to do is to get the derivative of the given functions with respect to their independent variables.
Take the derivative of the first equation with respect to u, we have
Take the derivative of the second equation with respect to u, we have
Since there are three variables in the given functions, then we have to use the Chain Rule in getting dy/dx, we have
Substitute the values of dy/du and dx/du to the above equation, we have
Since the two given equations have higher exponents and it's impossible to express each equations in terms of u, therefore
Category: Differential Calculus, Algebra
"Published in Vacaville, California, USA"
Given the following functions:
Find dy/dx.
Solution:
The first thing that we need to do is to get the derivative of the given functions with respect to their independent variables.
Take the derivative of the first equation with respect to u, we have
Take the derivative of the second equation with respect to u, we have
Since there are three variables in the given functions, then we have to use the Chain Rule in getting dy/dx, we have
Substitute the values of dy/du and dx/du to the above equation, we have
Since the two given equations have higher exponents and it's impossible to express each equations in terms of u, therefore
Category: Differential Calculus, Algebra
"Published in Vacaville, California, USA"
Find dy/dx by implicit differentiation for
Solution:
Consider the given equation above
Since the given equation is not a function, then we have to take the derivative of an equation with respect to y as follows
Therefore, by taking reciprocal on both sides of the equation,
We can also take the derivative of an equation by implicit differentiation as follows
which is the same as the first method.
