What is (\partial)/(\partial x)(5sin(3x)cos(4y)) ?

The answer to (\partial)/(\partial x)(5sin(3x)cos(4y)) is 15cos(3x)cos(4y)

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(\partial)/(\partial x)(5sin(3x)cos(4y))

\frac{\partial}{\partial x} (5 sin (3 x) cos (4 y))

15 cos (3 x) cos (4 y)

Solution steps

\frac{\partial}{\partial x} (5 sin (3 x) cos (4 y))

Treat

y

as a constant

Take the constant out:

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

= 5 cos (4 y) \frac{\partial}{\partial x} (sin (3 x))

Apply the chain rule:

cos (3 x) \frac{\partial}{\partial x} (3 x)

= cos (3 x) \frac{\partial}{\partial x} (3 x)

\frac{\partial}{\partial x} (3 x) = 3

= 5 cos (4 y) cos (3 x) \cdot 3

Simplify

= 15 cos (3 x) cos (4 y)

What is (\partial)/(\partial x)(5sin(3x)cos(4y)) ?
The answer to (\partial)/(\partial x)(5sin(3x)cos(4y)) is 15cos(3x)cos(4y)