Question

Find the first order partial derivative of the following function with respect to y ($\frac{\partial F}{\partial y} = F_y$) given $F = x^3y^4 + sinxcosy + xlny$. Now find the second order partial derivative with respect to x ($\frac{\partial^2 F}{\partial y\partial x} = F_{yx}$)

          Find the first order partial derivative of the following function with respect to y ($\frac{\partial F}{\partial y} = F_y$)
given $F = x^3y^4 + sinxcosy + xlny$.
Now find the second order partial derivative with respect to x ($\frac{\partial^2 F}{\partial y\partial x} = F_{yx}$)

Find the first order partial derivative of the following function with respect to y ((∂ F)/(∂ y) = Fy)
given F = x^3y^4 + sinxcosy + xlny.
Now find the second order partial derivative with respect to x ((∂^2 F)/(∂ y∂ x) = Fyx)

Added by Nicole R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Bhushan Arora

12/17/2021

Step 1

$F = x^3y^4 + sinxcosy + xlny$ $\frac{\partial F}{\partial y} = \frac{\partial}{\partial y}(x^3y^4 + sinxcosy + xlny)$ $\frac{\partial F}{\partial y} = 4x^3y^3 - sinxsiny + \frac{x}{y}$ Show more…

Show all steps

Thanks for your feedback!

Find the first order partial derivative of the following function with respect to y ($\frac{\partial F}{\partial y} = F_y$) given $F = x^3y^4 + sinxcosy + xlny$. Now find the second order partial derivative with respect to x ($\frac{\partial^2 F}{\partial y \partial x} = F_{yx}$)