Question

d/dx(sin(xyz)) please show all steps!

Answer 1

See if this helps:

http://www.wolframalpha.com/input/?i=d%2Fdx%28sin%28xyz%29%29

Click show steps.

Answer 2

thank you, i know how to calculate this way, but my book says the answer is cos(xyz)*(x(dz/dx)+z) can anyone help?

Answer 3

sorry, it's cos(xyz)*(y(dz/dx)+z)

Answer 4

sorry again, lol it's cos(xyz)*(y(dz/dx)+z))

Answer 5

I'm very rusty with this stuff ....
but should y and z be treated the same way ?
i.e. - something like below ?

cos(xyz)*( y*dz/dx + z*dy/dx )

Answer 6

let's wait for someone who knows what they're actually doing....
meanwhile I'll take a stab at it -

\[\frac{d}{dx}\sin(xyz)=\cos(xyz)*(\frac{d}{dx}(xyz))\]
\[=\cos(xyz)*(\frac{dx}{dx}yz+x\frac{dy}{dx}z+xy\frac{dz}{dx})\]
\[=\cos(xyz)*(yz+x\frac{dy}{dx}z+xy\frac{dz}{dx})\]

Answer 7

\[\frac{d}{dx} \sin(xyz) =\cos(xyz)* \frac{d}{dx}(xyz)\]your differentiating with respect to x so y an z are constants so they can be facctored out
=\[yz*\cos(xyz)\]

Answer 8

oh sory i just read the posts, ill do it the other way

Answer 9

yes - that's what wolfram said :)
but it looks like y and z are functions of x

Answer 10

you have to indicate whether the derivation is implicit or not

Answer 11

if its implicit; chain out the product rule

if it isnt implicity; treat yz as a constant

Answer 12

you have to be told which way they are wanting it to be done since both ways are acceptable solutions

Answer 13

according to johnjohn's comments it doesnt look like it.
at least not both of them.

He posted that the answer in his book is this:

cos(xyz)*(y(dz/dx)+z))

Answer 14

actually it's cos(xyz)*(y(x(dz/dx)+z))

and yes, it uses implicit derivatives