[SOLVED] Partial derivative ... check me plz

[rocomath]

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 :approve:

[rocomath]

Thanks Hootenanny :)

[Hootenanny]

Thanks Hootenanny :)

A pleasure as always roco :smile:

[Vid]

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