Use implicit differentiation to determine (del z)/(del x) in yz=ln(x+z) and sin(xyz)=x+2y+3z.

hogwartsxhoe5t

hogwartsxhoe5t

Answered question

2022-10-15

Use implicit differentiation to determine z x in y z = l n ( x + z ) and sin ( x y z ) = x + 2 y + 3 z.
Here is my answer:
y z = l n ( x + z )
y z = ( 1 + z ) 1 x + z
z = 1 y x + y z 1
and
sin ( x y z ) = x + 2 y + 3 z
y ( z + x z ) cos ( x y z ) = 1 + 3 z
y z cos ( x y z ) + x y z cos ( x y z ) = 1 + 3 z
y z cos ( x y z ) 1 = z ( 3 x y cos ( x y z ) )
z = y z cos ( x y z ) 1 3 x y cos ( x y z )
is that right?

Answer & Explanation

Besagnoe9

Besagnoe9

Beginner2022-10-16Added 9 answers

Not quite. Don't forget the chain rule, and to include other instances of y x .
For instance, in the first, don't forget that
x ( y z ) = y x z + y z x
and in the second, don't forget that
x ( x + 2 y + 3 z ) = 1 + 2 y x + 3 z x
Otherwise, your techniques look reasonably ok.

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