Partial Differentiation

Category: Differential Calculus, Algebra

"Published in Newark, California, USA"

If

show that

Solution:

Consider the given equation above

Take the partial derivative with respect to x, consider y as a constant, we have

Consider the given equation above again

Take the partial derivative with respect to y, consider x as a constant, we have

If

then

Therefore,

Differentiation - First Derivative

Category: Differential Calculus, Algebra

"Published in Newark, California, USA"

Find y' for the given value of x for

Solution:

Consider the given equation above

Simplify the numerator in order to avoid the confusion later for differentiation, we have

Take the derivative of the above equation with respect to x

If x = 1, then the value of y' is equal to

Implicit Differentiation

Category: Differential Calculus, Algebra

"Published in Suisun City, California, USA"

Find y" by implicit differentiation for

Solution:

Consider the given equation above

Since the given equation above is not a function, then we have to differentiate it by implicit differentiation as follows

but

or

then the above equation becomes

Rationalize the denominator in order to eliminate the radical sign at the denominator, we have

Take the derivative with respect to x, we have

Rationalize the denominator in order to eliminate the radical sign at the denominator, we have

Therefore,