COnsider the multivariable function g(x,y)=x^2-3y^4x^2+sin(xy). Find the following partial derivatives: g_x. g_y, g_(xy), g(xx), g(yy).

Sinead Mcgee

Sinead Mcgee

Answered question

2021-03-02

COnsider the multivariable function g(x,y)=x23y4x2+sin(xy). Find the following partial derivatives: gx.gy,gxy,g(×),g(yy).

Answer & Explanation

Theodore Schwartz

Theodore Schwartz

Skilled2021-03-03Added 99 answers

gx=x(x23y4x2+sinx)) [treat y as cons tant]
=2x6xy4+ycosxy
Again
gy=y(x23y4x2+sinxy) [treat x as cons tant]
=12x2y3+xcosxy
Now
gxx=x(gx)=x(2x6xy4+ycosxy)
=26y4y2sinxy
Again
gyy=y(12x2y3+xcosxy)
=36x2y2x2sinxy
Also
gxy=y(gx)
=y(2x6xy4+ycosxy)
=24xy3y2sinxy+cosxy

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Multivariable calculus

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?