What is (\partial)/(\partial x)(cos(12x)sin(4y)) ?

The answer to (\partial)/(\partial x)(cos(12x)sin(4y)) is -12sin(12x)sin(4y)

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(\partial)/(\partial x)(cos(12x)sin(4y))

\frac{\partial}{\partial x} (cos (12 x) sin (4 y))

- 12 sin (12 x) sin (4 y)

Solution steps

\frac{\partial}{\partial x} (cos (12 x) sin (4 y))

Treat

y

as a constant

Take the constant out:

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

= sin (4 y) \frac{\partial}{\partial x} (cos (12 x))

Apply the chain rule:

- sin (12 x) \frac{\partial}{\partial x} (12 x)

= - sin (12 x) \frac{\partial}{\partial x} (12 x)

\frac{\partial}{\partial x} (12 x) = 12

= sin (4 y) (- sin (12 x) \cdot 12)

Simplify

= - 12 sin (12 x) sin (4 y)

\frac{( - 3 )}{s ( s - 3 )}

\int (\frac{2 x}{1 + x ^{4}}) d x

\int cot^{2} (4 x) d x

f (x) = e^{x} + x^{e}

\frac{d}{d x} (sec (8 x))

What is (\partial)/(\partial x)(cos(12x)sin(4y)) ?
The answer to (\partial)/(\partial x)(cos(12x)sin(4y)) is -12sin(12x)sin(4y)