What is (\partial)/(\partial z)(10e^xsin(y)z^3) ?

The answer to (\partial)/(\partial z)(10e^xsin(y)z^3) is 30e^xz^2sin(y)

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(\partial)/(\partial z)(10e^xsin(y)z^3)

\frac{\partial}{\partial z} (10 e^{x} sin (y) z^{3})

30 e^{x} z^{2} sin (y)

Solution steps

\frac{\partial}{\partial z} (10 e^{x} sin (y) z^{3})

Treat

x, y

as constants

Take the constant out:

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

= 10 e^{x} sin (y) \frac{\partial}{\partial z} (z^{3})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 10 e^{x} sin (y) \cdot 3 z^{3 - 1}

Simplify

= 30 e^{x} z^{2} sin (y)

\frac{d}{d x} ((A x^{2} + B x + C) (e^{4 x}))

y^{^{'}} = \frac{2 y ^{4} - 2}{4 x y ^{3}}

n = 3 \sum \infty 1 + \frac{1}{n ^{2}}

x \cdot e^{x}

\frac{d}{d x} (x^{2} + \frac{1}{x})

What is (\partial)/(\partial z)(10e^xsin(y)z^3) ?
The answer to (\partial)/(\partial z)(10e^xsin(y)z^3) is 30e^xz^2sin(y)