More Integration Procedures, 8

Category: Integral Calculus

"Published in Newark, California, USA"

Evaluate

Solution:

Consider the given equation above

Convert each term into their equivalent exponential power, we have

All terms can be integrated by integration of powers

Substitute the value of limits and therefore, the answer is

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