What is (\partial)/(\partial y)(e^{xyz^9}yz^9) ?

The answer to (\partial)/(\partial y)(e^{xyz^9}yz^9) is z^9(e^{xyz^9}xyz^9+e^{xyz^9})

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(\partial)/(\partial y)(e^{xyz^9}yz^9)

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

z^{9} (e^{x y z^{9}} x y z^{9} + e^{x y z^{9}})

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x y z^{9}}, g = y

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

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

\frac{\partial}{\partial y} (y) = 1

= z^{9} (e^{x y z^{9}} x z^{9} y + 1 \cdot e^{x y z^{9}})

Simplify

= z^{9} (e^{x y z^{9}} x y z^{9} + e^{x y z^{9}})

\int 2 e^{4} d x

25 \frac{d ^{2} y}{d x ^{2}} - 10 \frac{d y}{d x} + y = 0

n = 0 \sum \infty \frac{n}{3 n + 1}

x \to 5 - lim (ln (5 - x))

x \to 0 lim (3 x^{n} \cdot sin (\frac{2}{x}))

What is (\partial)/(\partial y)(e^{xyz^9}yz^9) ?
The answer to (\partial)/(\partial y)(e^{xyz^9}yz^9) is z^9(e^{xyz^9}xyz^9+e^{xyz^9})