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!

What's happening?

The Chain Rule is happening!

d/dx(e^xsiny) = (d/dx(e^x)) siny + e^x(d/dx(siny))

 

[JFonseka]

Hi JFonseka!


The Chain Rule is happening!

d/dx(e^xsiny) = (d/dx(e^x)) siny + e^x(d/dx(siny))

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!


The Chain Rule is happening!

d/dx(e^xsiny) = (d/dx(e^x)) siny + e^x(d/dx(siny))

I think you mean the product rule?

 

[tiny-tim]

oops! ​

 

[BoundByAxioms]