"Published in Newark, California, USA"
Evaluate
Solution:
Consider the given equation above
The first thing that we have to do is to square the binomial, we have
Therefore,
where C is the constant of integration.
This website will show the principles of solving Math problems in Arithmetic, Algebra, Plane Geometry, Solid Geometry, Analytic Geometry, Trigonometry, Differential Calculus, Integral Calculus, Statistics, Differential Equations, Physics, Mechanics, Strength of Materials, and Chemical Engineering Math that we are using anywhere in everyday life. This website is also about the derivation of common formulas and equations. (Founded on September 28, 2012 in Newark, California, USA)
Wednesday, March 5, 2014
Integration - Algebraic Functions, Powers, 15
Category: Integral Calculus, Algebra
"Published in Newark, California, USA"
Evaluate
Solution:
Consider the given equation above
The first thing that we have to do is to square the binomial, we have
Therefore,
where C is the constant of integration.
"Published in Newark, California, USA"
Evaluate
Solution:
Consider the given equation above
The first thing that we have to do is to square the binomial, we have
Therefore,
where C is the constant of integration.
Tuesday, March 4, 2014
Integration - Algebraic Functions, Powers, 14
Category: Integral Calculus, Algebra
"Published in Newark, California, USA"
Evaluate
Solution:
Consider the given equation above
The first thing that we need to do is to rewrite the radical sign into its equivalent fractional exponent as follows
Therefore,
where C is the constant of integration.
"Published in Newark, California, USA"
Evaluate
Solution:
Consider the given equation above
The first thing that we need to do is to rewrite the radical sign into its equivalent fractional exponent as follows
Therefore,
where C is the constant of integration.
Monday, March 3, 2014
Second Derivative Problems - Chain Rule
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
"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
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