Question
Asked Nov 5, 2019
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Find the gradient for the function f(x, y) = x5 sin(xy) at the point (, 10)
Find exact values. No decimal entries.
Vf(T, 10)
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Find the gradient for the function f(x, y) = x5 sin(xy) at the point (, 10) Find exact values. No decimal entries. Vf(T, 10)

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Expert Answer

Step 1

To find the gradient of a function (which is a vector), differentiate the function with respect to each variable.

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Vf =

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Step 2

Find partial derivative of f w.r.t. x

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дf дх д (х'sin(xy)) дх д е (sin(xy) (х) sin(xy)+x5. дх дх д %35x'sin(xy)+x'cos(ху). (ху) дх 35x'sin(xy)+x'cos(ху) (у) —х"[5sin(xy)+xycos(ху)]

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Step 3

Find partial derivative of f ...

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Of ду -(x'sin(xy) ду (x)sin(xy)+x ду (sin(xy)) ду (0)sin(xy)+x'cos(xy) (ху) ду =0+x°cos(xy)(x) =x°cos(xy)

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