Solving Exponential Equation

Category: Algebra

"Published in Suisun City, California, USA

Find the value of x for

Solution:

Consider the give equation

Rewrite the above equation as follows

Take the natural logarithm on both sides of the equation

Therefore,

Your Ad Here

Simplifying Algebraic Expression - Radical Group

Category: Algebra

"Published in Suisun City, California, USA"

Simplify the expression for:

Solution:

Consider the given equation

Square the term first inside the parenthesis

Get the LCD of the two terms inside the radical sign and combine all the terms in the numerator

Rationalize the denominator in order to remove the radical sign by multiplying both sides of the fraction by the denominator, we have

Partial Differentiation - Three Variables

Category: Differential Calculus

"Published in Newark, California, USA"

If

show that 

Solution:

If you will take the partial derivative of a function with respect to a certain variable, then the other variables will be treated as a constant. Consider the given equation

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

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

To prove that

Substitute the values of the partial derivative and the value of z to the above equation, we have

Therefore,