What is (\partial)/(\partial x)(2e^{xyz}sin(xw)) ?

The answer to (\partial)/(\partial x)(2e^{xyz}sin(xw)) is 2(e^{xyz}yzsin(xw)+cos(xw)we^{xyz})

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(\partial)/(\partial x)(2e^{xyz}sin(xw))

\frac{\partial}{\partial x} (2 e^{x yz} sin (x w))

2 (e^{x yz} yz sin (x w) + cos (x w) w e^{x yz})

Solution steps

\frac{\partial}{\partial x} (2 e^{x yz} sin (x w))

Treat

y, z, w

as constants

Take the constant out:

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

= 2 \frac{\partial}{\partial x} (e^{x yz} sin (x w))

Apply the Product Rule:

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

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

= 2 (\frac{\partial}{\partial x} (e^{x yz}) sin (x w) + \frac{\partial}{\partial x} (sin (x w)) e^{x yz})

\frac{\partial}{\partial x} (e^{x yz}) = e^{x yz} yz

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

= 2 (e^{x yz} yz sin (x w) + cos (x w) w e^{x yz})

\int_{2}^{5} \frac{1}{x} d x

x^{2} - 1

\int_{1}^{4} 8 x ln (x) d x

\int (x^{3} + 4 x y) d x

\int_{0}^{1} (x^{2} + 1) (e^{- x}) d x

What is (\partial)/(\partial x)(2e^{xyz}sin(xw)) ?
The answer to (\partial)/(\partial x)(2e^{xyz}sin(xw)) is 2(e^{xyz}yzsin(xw)+cos(xw)we^{xyz})