Category: Differential Calculus, Algebra
"Published in Newark, California, USA"
If y = f(u) and u = ϕ(x), show that
Solution:
Consider the given two equations above
Since y is a function of u and u is a function of x, then we can apply the derivative of y with respect to x by Chain Rule Method.
Take the derivative of the first equation with respect to u, we have
Take the derivative of the second equation with respect to x, we have
Hence, by Chain Rule Method,
Take the derivative of the above equation with respect to x, we have
but
Hence, the above equation becomes
Therefore,
where
Category: Differential Calculus, Algebra
"Published in Vacaville, California, USA"
Using the fact that
show that
Solution:
Consider the given equation above
Take the derivative on both sides of the equation with respect to x by quotient formula, we have
Therefore,
Category: Differential Calculus, Algebra
"Published in Vacaville, California, USA"
Find a formula for
Solution:
The
first thing that we have to do is to get the derivative of u/v with
respect to x where u and v are functions of x. Apply the derivative by quotient formula, we have
Take the derivative again of the above equation with respect to x by product formula, we have
where:
