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

The answer to (\partial)/(\partial x)(9e^{sqrt(xy)}) is (9e^{sqrt(xy)}sqrt(y))/(2sqrt(x))

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

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

\frac{9 e ^{x y} y}{2 x}

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) = \frac{1}{2 x y} y

= 9 e^{x y} \frac{1}{2 x y} y

Simplify

9 e^{x y} \frac{1}{2 x y} y : \frac{9 e ^{x y} y}{2 x}

= \frac{9 e ^{x y} y}{2 x}

\frac{d}{d x} ((e^{l n (x)})^{2^{- x}})

\int \frac{12}{x ^{2} - 1} d x

\frac{d}{d x} (\frac{6 x}{e ^{x}})

\int x^{2} cos (w x) d x

f (I) = \frac{110 I}{I ^{2} + I + 1}

What is (\partial)/(\partial x)(9e^{sqrt(xy)}) ?
The answer to (\partial)/(\partial x)(9e^{sqrt(xy)}) is (9e^{sqrt(xy)}sqrt(y))/(2sqrt(x))