What is (\partial)/(\partial x)(2sin(5x)cos(4y)) ?

The answer to (\partial)/(\partial x)(2sin(5x)cos(4y)) is 10cos(5x)cos(4y)

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(\partial)/(\partial x)(2sin(5x)cos(4y))

\frac{\partial}{\partial x} (2 sin (5 x) cos (4 y))

10 cos (5 x) cos (4 y)

Solution steps

\frac{\partial}{\partial x} (2 sin (5 x) cos (4 y))

Treat

y

as a constant

Take the constant out:

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

= 2 cos (4 y) \frac{\partial}{\partial x} (sin (5 x))

Apply the chain rule:

cos (5 x) \frac{\partial}{\partial x} (5 x)

= cos (5 x) \frac{\partial}{\partial x} (5 x)

\frac{\partial}{\partial x} (5 x) = 5

= 2 cos (4 y) cos (5 x) \cdot 5

Simplify

= 10 cos (5 x) cos (4 y)

\int sin^{2} (t) cos^{2} (t) d t

\frac{d}{d x} (x^{6 c o s (x)})

\frac{2}{1 + x ^{2}}

y^{^{'}} + y = e^{3 x}

\frac{d}{d x} (3^{x - 1})

What is (\partial)/(\partial x)(2sin(5x)cos(4y)) ?
The answer to (\partial)/(\partial x)(2sin(5x)cos(4y)) is 10cos(5x)cos(4y)