SOLUTION: Find the derivative of 5/x²+3 using first derivative method.

Algebra ->  Test -> SOLUTION: Find the derivative of 5/x²+3 using first derivative method.      Log On


   

Question 1203112: Find the derivative of 5/x²+3 using first derivative method.
Found 3 solutions by Alan3354, ikleyn, math_tutor2020:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the derivative of 5/x²+3 using first derivative method.
----------------
Is it %285%2Fx%5E2%29+%2B+3
or 5%2F%28x%5E2%2B3%29 ?

Answer by ikleyn(52910) About Me  (Show Source):
You can put this solution on YOUR website!
.

As far as I know Calculus, there is a term  " first derivative "  there,
but there is no such term as  " first derivative method ".


If you would like to refute my statement,  then refer please to this combination of words
" first derivative method "  in some peer reviewed published  Calculus textbook,  or handbook,  or encyclopedia.



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

The expression you provided is vague.

Is it 5%2F%28x%5E2%29+%2B+3?

Or is it 5%2F%28x%5E2+%2B+3%29?

5%2F%28x%5E2%29+%2B+3 when written on a keyboard is 5/(x^2)+3

5%2F%28x%5E2+%2B+3%29 when written on a keyboard is 5/(x^2+3)

Pay careful attention to the placement of the parenthesis.

-------------------------------

If y = 5/(x^2) + 3, then,

y = 5/(x^2) + 3
y = 5x^(-2) + 3
dy/dx = d/dx[ 5x^(-2) + 3 ]
dy/dx = d/dx[ 5x^(-2) ] + d/dx[ 3 ]
dy/dx = 5*d/dx[ x^(-2) ] + d/dx[ 3 ]
dy/dx = 5*(-2)*x^(-2-1) + 0
dy/dx = -10x^(-3)
dy/dx = -10/(x^3)


OR
If y = 5/(x^2+3), then,

y = 5/(x^2+3)
y = 5(x^2+3)^(-1)
dy/dx = d/dx[ 5(x^2+3)^(-1) ]
dy/dx = 5*d/dx[ (x^2+3)^(-1) ]
dy/dx = 5*(-1)*(x^2+3)^(-1-1) * d/dx[ x^2+3 ]
dy/dx = 5*(-1)*(x^2+3)^(-2) *(2x)
dy/dx = -10x(x^2+3)^(-2)
dy/dx = -10x/( (x^2+3)^2 )

GeoGebra's CAS tool, WolframAlpha, or similar tools can be used to verify these answers.