Need help with the following question Compute the directional derivative of

Wribreeminsl 2021-09-11 Answered

Need help with the following question Compute the directional derivative of
\(\displaystyle f{{\left({x},{y}\right)}}={e}^{2}{x}-{5}{y}\)

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Expert Answer

falhiblesw
Answered 2021-09-12 Author has 18287 answers

Possible derivation:
\(\displaystyle\frac{d}{{\left.{d}{x}\right.}}{\left({e}^{2}{x}-{5}{y}\right)}\)
Differentiate the sum term by term and factor out constants:
\(\displaystyle={e}^{2}{\left(\frac{d}{{\left.{d}{x}\right.}}{\left({x}\right)}\right)}+\frac{d}{{\left.{d}{x}\right.}}{\left(-{5}{y}\right)}\)
The derivative of x is 1:
\(\displaystyle=\frac{d}{{\left.{d}{x}\right.}}{\left(-{5}{y}\right)}+{1}{e}^{2}\)
The derivative of -5 y is zero:
\(\displaystyle={e}^{2}+{0}\)
Simplify the expression:
Answer:
\(\displaystyle={e}^{2}\)

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