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})

\int x + 5 d x

\frac{- x ^{2}}{2}

\frac{d}{d x} (- 8 e^{- 4 x^{2}} x)

\int \frac{1}{1 + e ^{- y}} d y

f (x) = (x + x^{- 1})^{3}

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))