# Partial derivatives - textbook error?

1. Aug 14, 2008

### 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?

2. Aug 14, 2008

### uman

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

3. Aug 14, 2008

### JFonseka

e^x ?

4. Aug 14, 2008

### uman

Try again.

5. Aug 14, 2008

### JFonseka

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

6. Aug 14, 2008

### Defennder

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

7. Aug 14, 2008

### tiny-tim

Hi JFonseka!
The Chain Rule is happening!

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

8. Aug 14, 2008

### JFonseka

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

9. Aug 14, 2008

### JFonseka

Nvm I get it now.

10. Aug 14, 2008

### JFonseka

Thanks to all who helped

11. Aug 14, 2008

### BoundByAxioms

I think you mean the product rule?

12. Aug 14, 2008

### tiny-tim

oops!

13. Aug 14, 2008