I’m really trying to figure out how to use your program with a couple different problem examples:
“Find the following derivatives of f(x). Do not leave any negative exponents”
1. F(x)= 4^x-ln(2x^2-x)
What program can I use to solve this?
another is f(x)=2csc(x)+5arccos(x)
This is fundamental to calculus and you must start to learn it or know it.
Notice the minus sign between the terms (if a plus no difference)
This means that the derivatives of the terms are separate or individual
You differentiate each by itself and one at a time
There could be 15 more terms each separated by a minus or plus and you’d do each one separate.
So: f(x) = 4^x f’(x) = x*4^(x-1) Notice when differentiating you take the exponent
Multiply it times the front of the term and take one away from the exponent.
You must do this process in your sleep and fast or you’ll have trouble passing calculus
Another Example
f(x) = 15x^7
f ‘(x) = derivative
= 7*15*x^(7-1)
= 105x^6
Integration is the exact opposite
You add one to the exponent first
Then divide by that new exponent
∫[105*x^6] dx
= 6+1 = 7
So: 105*x^7 / 7
= 15x^6
Problem 1) the trig problem
Reload the attached program
First Delete the same named program from you calculator
Then reload the attached changing to “Archives” first
For the problem go to:
“trig” in my menu
Scroll to csc(x)
Find the derivative and add the 2 in the front of the answer
For arcos(x)
Scroll to cos-1 in the menu of trig
And find that derivative adding the 5 in front
“Answer the following questions about the given function: f(x)=x^3-6x^2+9
A) Find f'(x)
B) Find f”(x)
These again are separated by minus and plus signs so each is differentiated separately
f(x) = x^3 – 6*x^2 + 9
f ’(x) = 3x^2 – 12x + 0
f ‘’ (x) = 6x – 12
Notice I took the exponent and multiplied it by the front of the term
And then took one away from the exponent in each case.
Do these in your sleep!!!!!
Use log differentiation to find the derivative of the following function with respect to variable x.
(x^3+2)^3sqrt(2x^2+3)
Notice the “times” sign so you’d be thinking “product rule” or logs to differentiate
First it must be expanded:
I have expanded log problems to another base
But haven’t programmed to expand natural logs, but am in the process.
Should be done soon
(x^3+2)^3 * √(2*x^2+3
ln((x^3+2)^3) + ln(√(2*x^2+3) (always you change a square root to ^(1/2)
= ln( (x^3+2)^3 ) + ln( (2*x^2+3)^(1/2) )
= 3*ln( x^3+2 ) + (1/2)*ln( 2*x^2+3 )
Now you can choose in my menu
“log Problems”
Choose “ln(x)”
Choose “differentiate”
And add the above ln tems one at a time
Put the problem back together when finished with the individual solutions.
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