Partial derivatives - textbook error?

[JFonseka]

Now in my textbook it shows the following partial derivative solution:

\frac{d}{dx}(3y^{4} + e^{x} sin y) = e^{x} sin y

I thought since it's meant to be the partial derivative in terms of x that the y variable would be untouched.

What's happening?

[uman]

What's the first derivative of f(x) = 3*(5^4) + e^x * sin(5)?

[JFonseka]

What's the first derivative of f(x) = 3*(5^4) + e^x * sin(5)?

e^x ?

[uman]

Try again.

[JFonseka]

Try again.

Huh? What else can it be, the rest are all constants.

[Defennder]

If a constant is multiplied to f(x), it doesn't become 1 after differentiating them both.

[tiny-tim]

Hi JFonseka! :smile:
What's happening?

The Chain Rule is happening!

d/dx(exsiny) = (d/dx(ex)) siny + ex(d/dx(siny)) :smile:

[JFonseka]

Hi JFonseka! :smile:


The Chain Rule is happening!

d/dx(exsiny) = (d/dx(ex)) siny + ex(d/dx(siny)) :smile:

I get that bit lol, but I don't get why 3y^4 disappeared,

[JFonseka]

Nvm I get it now.

[JFonseka]

Thanks to all who helped

[BoundByAxioms]

Hi JFonseka! :smile:


The Chain Rule is happening!

d/dx(exsiny) = (d/dx(ex)) siny + ex(d/dx(siny)) :smile:

I think you mean the product rule?

[tiny-tim]

:redface: oops! :redface:

[BoundByAxioms]

:wink: