What is (\partial)/(\partial x)(9e^{xy}) ?

The answer to (\partial)/(\partial x)(9e^{xy}) is 9e^{xy}y

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(\partial)/(\partial x)(9e^{xy})

\frac{\partial}{\partial x} (9 e^{x y})

9 e^{x y} y

Solution steps

\frac{\partial}{\partial x} (9 e^{x y})

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 9 \frac{\partial}{\partial x} (e^{x y})

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x y) = y

= 9 e^{x y} y

\frac{1}{2} x^{2}, - x^{2} + 6

y = x^{2} + 1, y = x + 3, (- 1, 2)

\frac{1}{s ( s + 1 )}

\frac{d}{d x} (c cos (t) + t^{2} sin (t))

e^{x^{2}} \cdot \frac{1}{2}

What is (\partial)/(\partial x)(9e^{xy}) ?
The answer to (\partial)/(\partial x)(9e^{xy}) is 9e^{xy}y