What is (\partial)/(\partial x)(4sin(6x-7y)) ?

The answer to (\partial)/(\partial x)(4sin(6x-7y)) is 24cos(6x-7y)

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(\partial)/(\partial x)(4sin(6x-7y))

\frac{\partial}{\partial x} (4 sin (6 x - 7 y))

24 cos (6 x - 7 y)

Solution steps

\frac{\partial}{\partial x} (4 sin (6 x - 7 y))

Treat

y

as a constant

Take the constant out:

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

= 4 \frac{\partial}{\partial x} (sin (6 x - 7 y))

Apply the chain rule:

cos (6 x - 7 y) \frac{\partial}{\partial x} (6 x - 7 y)

= cos (6 x - 7 y) \frac{\partial}{\partial x} (6 x - 7 y)

\frac{\partial}{\partial x} (6 x - 7 y) = 6

= 4 cos (6 x - 7 y) \cdot 6

Simplify

= 24 cos (6 x - 7 y)

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What is (\partial)/(\partial x)(4sin(6x-7y)) ?
The answer to (\partial)/(\partial x)(4sin(6x-7y)) is 24cos(6x-7y)