What is the derivative of e^{xy} ?

The derivative of e^{xy} is e^{xy}(y+x(dy)/(dx))

What is the first derivative of e^{xy} ?

The first derivative of e^{xy} is e^{xy}(y+x(dy)/(dx))

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\frac{d}{d x} (e^{x y})

e^{x y} (y + x \frac{d y}{d x})

Solution steps

\frac{d}{d x} (e^{x y})

Apply the chain rule:

e^{x y} \frac{d}{d x} (x y)

= e^{x y} \frac{d}{d x} (x y)

\frac{d}{d x} (x y) = y + x \frac{d y}{d x}

= e^{x y} (y + x \frac{d y}{d x})

7 x^{2} y^{4} (12 x^{3} y)

e^{- 2 ∣ t ∣}

e^{- x} e^{x}

\frac{( x + 1 ) ^{2}}{x ^{2}}

2^{8}

What is the derivative of e^{xy} ?
The derivative of e^{xy} is e^{xy}(y+x(dy)/(dx))
What is the first derivative of e^{xy} ?
The first derivative of e^{xy} is e^{xy}(y+x(dy)/(dx))