What is (\partial)/(\partial x)(cos(2x)sin(3y)) ?

The answer to (\partial)/(\partial x)(cos(2x)sin(3y)) is -2sin(2x)sin(3y)

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(\partial)/(\partial x)(cos(2x)sin(3y))

\frac{\partial}{\partial x} (cos (2 x) sin (3 y))

- 2 sin (2 x) sin (3 y)

Solution steps

\frac{\partial}{\partial x} (cos (2 x) sin (3 y))

Treat

y

as a constant

Take the constant out:

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

= sin (3 y) \frac{\partial}{\partial x} (cos (2 x))

Apply the chain rule:

- sin (2 x) \frac{\partial}{\partial x} (2 x)

= - sin (2 x) \frac{\partial}{\partial x} (2 x)

\frac{\partial}{\partial x} (2 x) = 2

= sin (3 y) (- sin (2 x) \cdot 2)

Simplify

= - 2 sin (2 x) sin (3 y)

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 1

\frac{d ^{2} y}{d x ^{2}} = 4 x cos (x^{2})

3 y^{^{'}} + y = (1 - 2 x) y^{4}

y = \frac{- 1}{3 x ^{2}}

\frac{d}{d x} (3 x - 4 x^{3} + 2^{x} - e + 7)

What is (\partial)/(\partial x)(cos(2x)sin(3y)) ?
The answer to (\partial)/(\partial x)(cos(2x)sin(3y)) is -2sin(2x)sin(3y)