Find the indicated partial derivative. f ( x , y ) = 4 x y 8 + x 8 y 5 f x x y = blank f y...

Question:

Find the indicated partial derivative.

{eq}f(x,y) = 4xy^{8}+x^{8}y^{5} {/eq}

{eq}f_{x} {/eq} {eq}_{x} {/eq} {eq}_{y} = \square {/eq}

{eq}f _{y} {/eq} {eq}_{y} {/eq} {eq}_{y} = \square {/eq}

Partial Derivative:

Given the function f(x,y) for finding the partial derivative of f with respect to x i.e. {eq}f_x(x,y) {/eq} differentiate f(x,y) with respect to x keeping y as constant. For finding {eq}f_{xx} {/eq} differentiate {eq}f_x(x,y) {/eq} with respect to x keeping y as constant. For finding {eq}f_{xxy} {/eq} differentiate {eq}f_xx(x,y) {/eq} with respect to y keeping x as constant.

Answer and Explanation:

{eq}f(x,y) = 4xy^{8}+x^{8}y^{5}\\ f_x(x,y) = 4y^{8} + 8x^7 y^5\\ f_{xx} (x,y)= 56 x^6 y^5 \\ f_{xxy} (x,y) =280 x^6 y^4\\ f_y (x,y) = 32 x y^7 + 5x^8y^4\\ f_{yy}(x,y) = 224xy^6 + 20 x^8 y^3\\ f_{yyy}(x,y) = 1344 xy^5 + 60 x^8 y^2\\ {/eq}

Learn more about this topic:

Solving Partial Derivative Equations

from GRE Math: Study Guide & Test Prep

Chapter 14 / Lesson 1
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