What is (\partial)/(\partial z)(ye^zsin(xz)) ?

The answer to (\partial)/(\partial z)(ye^zsin(xz)) is y(e^zsin(xz)+cos(xz)xe^z)

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(\partial)/(\partial z)(ye^zsin(xz))

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

y (e^{z} sin (x z) + cos (x z) x e^{z})

Solution steps

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

Treat

y, x

as constants

Take the constant out:

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

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

Apply the Product Rule:

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

f = e^{z}, g = sin (x z)

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

\frac{\partial}{\partial z} (e^{z}) = e^{z}

\frac{\partial}{\partial z} (sin (x z)) = cos (x z) x

= y (e^{z} sin (x z) + cos (x z) x e^{z})

x \to - \infty lim (5 f (x))

2 (1 - e^{- 1 t})

f (x, y) = x e^{x - y}

\int \frac{4 x ^{3} - 6 x}{e ^{2 x^{2}}} d x

What is (\partial)/(\partial z)(ye^zsin(xz)) ?
The answer to (\partial)/(\partial z)(ye^zsin(xz)) is y(e^zsin(xz)+cos(xz)xe^z)