Good Day Class! Today I will be teaching the class about
Derivatives! Derivatives are the way we find a certain point, so another words,
we are finding the slope of a particular point! Pretty exciting stuff right?!
These points are found using the derivative of the equation, which, by the way,
is also shown by the tangent line.
Now that we are super pumped up about derivatives, let’s
look at all the different rule that we use when fining them….. This makes
things much easier to understand
These rules are:
Constant Function- Used when looking for the derivative of a constant
example:
y=x
d/dx(x)=0
Linear Function- Used for a linear equation in the form y=mx+b
example:
y=4/5x+5
d/dx=4/5+0
The Power Rule- Used when the equation is raised to a power
d/dx(x^n)= nX^n-1
example- d/dx (4x^2)= 8x
These rules are:
Constant Function- Used when looking for the derivative of a constant
example:
y=x
d/dx(x)=0
Linear Function- Used for a linear equation in the form y=mx+b
example:
y=4/5x+5
d/dx=4/5+0
The Power Rule- Used when the equation is raised to a power
d/dx(x^n)= nX^n-1
example- d/dx (4x^2)= 8x
A function multiplied by a constant: In this case the
derivative of the formula is multiplied by a constant.
Sum & Difference- Used when functions are being added or subtracted
example:
d/dx[f(x)+g(x)]= d/dx(f(x))+ d/dx(g(x))
d/dx[f(x)-g(x)]=d/dx(f(x))- d/dx(g(x))
Sum & Difference- Used when functions are being added or subtracted
example:
d/dx[f(x)+g(x)]= d/dx(f(x))+ d/dx(g(x))
d/dx[f(x)-g(x)]=d/dx(f(x))- d/dx(g(x))
The Natural Exponent Rule- Used when the equation is a natural number raised to a power
d/dx(e^x)= e^x
example: f(x)= 7e^x-12x---- d/dx=7e^x-(ln12)(12^x)
Derivative of Lnx- Used when find the derivative of a natural log
d/dx (fx)=lnx= 1/x
Product Rule- (f(x) x g(x)) = f(x)` x g(x) + g(x)` x f(x)
Quotient Rule- f(x)/g(x)= f(x)` x g(x) - f(x) x g(x)`/g(x)^2
Using these rules not only makes fining the derivative much easier, but easier to understand
So… to recap…. Remember these basics when looking at an equation that you are trying to find the derivative of….
A constant is always Zero!
The power rule is easy and makes computations easy too! Just take the original power, multiply if in front of its original and is one less the power
2^4 becomes 4^3 as its derivative.
Once you remember the rules, the computations are easy! See derivatives are fun!
Once you remember the rules, the computations are easy! See derivatives are fun!
The equations and rules were broken up really easily. Explanations were also really easy to follow.
ReplyDeleteYour blog/lesson is really well written and easy to follow. You cleanly covered a lot of material - good job!
ReplyDeletegood job I think derivatives are fun too once you understand them
ReplyDeleteGood job Shannon! Your lecture was interesting and fascinating to read! You explained the derivatives nicely for others to understand.
ReplyDeleteshannon,
ReplyDeletegood job on your lesson. i liked your introduction! you did a good job of showing the rules for derivatives, however, a few more examples for some of them would have been nice to see. i like your little tricks at the end of the lesson.
the only thing i want to caution on is the formula you used for the constant function. y=x is actually the formula for a linear function with slope 1 and y-int (0,0). it's more accurate to use "c" or "k" when talking about a constant.
other than that, really nice job!
professor little
Very interesting . really nice job
ReplyDelete