 # 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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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:
$$\displaystyle={e}^{2}$$