What is the partial derivative of f(x,y) with respect to x?

[rocomath]

[SOLVED] Partial derivative ... check me please

$$f(x,y)=\sqrt[5]{x^7y^4}$$

$$f_x(x,y)=\frac 1 5(x^7y^4)^{-\frac{4}{5}}(7x^6y^4)$$

$$f_x(x,y)=\frac{7x^6y^4}{5\sqrt[5]{x^7y^4}}$$

Correct?

 

[Hootenanny]

$$f(x,y)=\sqrt[5]{x^7y^4}$$

$$f_x(x,y)=\frac 1 5(x^7y^4)^{-\frac{4}{5}}(7x^6y^4)$$

$$f_x(x,y)=\frac{7x^6y^4}{5\sqrt[5]{x^7y^4}}$$

Correct?

I don't think so.

HINT:

$$f(x,y) = x^{7/5}y^{4/5}$$

 

[rocomath]

I don't think so.

HINT:

$$f(x,y) = x^{7/5}y^{4/5}$$

omg ... I'm embarassed :D

ok so ...

$$f_x(x,y)=\frac 7 5x^{\frac 2 5}y^{\frac 4 5}$$

 

[Hootenanny]

omg ... I'm embarassed :D

ok so ...

$$f_x(x,y)=\frac 7 5x^{\frac 2 5}y^{\frac 4 5}$$

Sounds good to me

 

[rocomath]

Thanks Hootenanny :)

 

[Hootenanny]

Thanks Hootenanny :)

A pleasure as always roco

 

[Vid]

You would have gotten the same answer, but the denominator has the wrong exponent.