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)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\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)

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)