Derivatives

[MWR]

Could someone double-check my answers to these derivative problems?

-- f(x) = e^(x^3 + 2)

= 3x^2 e^(x^3 + 2)


-- f(x) = (e^-4x)/(x^3 + 7)

= e^-4x [(-4x^3 - 3x^2 - 28)/(x^3 + 7)^2]


-- f(x) = x^3 ln x

= 3x^2 ln(x) + x^2


-- f(x) = (ln^3 sqrt(x^2))/(x^3)

= (ln)3


-- f(x) = (^7 sqrt(x+8))/(5-6x)^8)

= [(x+8)/(5-6x)^8)] [(1/7) (1/x+8) + (48/5-6x)]


Thanks in advance for any help.

 

[Jameson]

For double checking things like this, I highly suggest using Wolfram Alpha. For example, here is the output for the first derivative you listed.

 

[HallsofIvy]

If I were your teacher, I would mark everyone of them wrong.

You are asked to find the derivative of f and have, for example,
f(x) = e^(x^3 + 2)

= 3x^2 e^(x^3 + 2)

where, for some reason, you have said that f(x) is equal to 3x^2 e^(x^3+ 2) but have NOT said what the derivative of f is equal to!

 

[Ackbach]

If I were your teacher, I would mark everyone of them wrong.

You are asked to find the derivative of f and have, for example,
f(x) = e^(x^3 + 2)

= 3x^2 e^(x^3 + 2)

where, for some reason, you have said that f(x) is equal to 3x^2 e^(x^3+ 2) but have NOT said what the derivative of f is equal to!

Definitely second this. It is quite simply not enough to have the correct answer. You must present it as such; and your presentation must be logical and straight-forward.