What is (\partial)/(\partial y)(6xsin(y-z)) ?

The answer to (\partial)/(\partial y)(6xsin(y-z)) is 6xcos(y-z)

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(\partial)/(\partial y)(6xsin(y-z))

\frac{\partial}{\partial y} (6 x sin (y - z))

6 x cos (y - z)

Solution steps

\frac{\partial}{\partial y} (6 x sin (y - z))

Treat

x, z

as constants

Take the constant out:

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

= 6 x \frac{\partial}{\partial y} (sin (y - z))

Apply the chain rule:

cos (y - z) \frac{\partial}{\partial y} (y - z)

= cos (y - z) \frac{\partial}{\partial y} (y - z)

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

= 6 x cos (y - z) \cdot 1

Simplify

= 6 x cos (y - z)

x^{3} cos (2 x)

\frac{d}{d x} (e^{2 x} \cdot sin (3 x))

\frac{1}{e ^{\frac{1}{x} + 1} - 1}

\int \frac{1}{x ^{2} 9 - x ^{2}} d x

\frac{- x ^{2} - 6}{( x ^{2} - 6 ) ^{2}}

What is (\partial)/(\partial y)(6xsin(y-z)) ?
The answer to (\partial)/(\partial y)(6xsin(y-z)) is 6xcos(y-z)