SOLUTION: 1) Let f(t)=(t^2+6t+4)(2t^2+5)
f'(t)=
f'(2)=
2) f(x)=4x / √8x2+5x−5.
Evaluate f′(x) at x=2
f′(2) =
.
3) Suppose that y=5(x2+6x)−1.
F
Algebra.Com
Question 1112736: 1) Let f(t)=(t^2+6t+4)(2t^2+5)
f'(t)=
f'(2)=
2) f(x)=4x / √8x2+5x−5.
Evaluate f′(x) at x=2
f′(2) =
.
3) Suppose that y=5(x2+6x)−1.
Find dy / dx =
4) Find f′(x) if
f(x)=(4x−4)^2⋅(3x^2+7)^2.
5) Differentiate y=(x^2+5 / x^2−5)^2.
dy / dx=
.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
One problem per post.
5. ^2}{\(x^2\ -\ 5\)^2}\] )
Let 
and let 
By the quotient rule
By the chain rule
But 
So substituting back:
\(x^2\ -\ 5\)^2\ -\ 4x\(x^2\ -\ 5\)\(x^2\ +\ 5\)^2}{\(x^2\ -\ 5\)^4)
A little more algebra...
^2}{\(x^2\ -\ 5\)^2}\]\ =\ -\frac{40\(x^2\ +\ 5\)}{\(x^\ -\ 5\)^3})
John
My calculator said it, I believe it, that settles it
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