Assume that y is a function of x. Find (dy)/(dx) for x^3+cos^3(y)=5x

Kade Rosales

Kade Rosales

Answered question

2022-08-11

Question:
Assume that y is a function of x. Find d y d x for x 3 + cos 3 ( y ) = 5 x

My first move, using the chain rule, is:
3 x 2 + 3 cos 2 ( y ) ( sin ( y ) ) = 5
However the text says this should instead be:
3 x 2 + 3 cos 2 ( y ) ( sin ( y ) ) d y d x = 5
I don't understand where or how the d y d x is being introduced.
To my mind, cos 3 ( y )= ( cos ( y ) ) 3 and so could be interpreted as:
f ( x ) = x 3
g ( x ) = cos ( y )
F ( x ) = f ( g ( x ) ) = cos 3 ( y )
Then, using the Chain Rule:
F ( x ) = f ( g ( x ) ) g ( x ) = 3 cos 2 ( y ) ( sin ( y ) )
But apparently that's wrong.

Answer & Explanation

Barbara Klein

Barbara Klein

Beginner2022-08-12Added 19 answers

by the chaine rule we get 3 x 2 + 3 cos ( y ( x ) ) 2 ( sin ( y ( x ) ) y ( x ) = 5
cofak48

cofak48

Beginner2022-08-13Added 2 answers

So we can read c o s 3 ( y ) as c o s 3 ( y ( x ) )

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?