Partial Derivatives

Question

Find the partial derivatives indicated Assume the variables are restricted to a domain on which the function is defined.

z=x⁷+5^y+x^y

z_x=

z_y=

Answer 1

Hint:

Z(x) : hold "y" constant -- treat it as a known constant, letting only x be a variable.

Z(y) : hold "x" constant -- treat it as a known constant, letting only y be a variable.

Regards,

Phil C.

Answer 2

Find the partial derivatives indicated Assume the variables are restricted to a domain on which the function is defined.

z=x⁷+5^y+x^y

z_x= 7x⁶ +y( x^y-1)

z_{y =} 5^y ln5 + x^y ln x