What is (\partial)/(\partial y)(8xcos(3xy)) ?

The answer to (\partial)/(\partial y)(8xcos(3xy)) is -24x^2sin(3xy)

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(\partial)/(\partial y)(8xcos(3xy))

\frac{\partial}{\partial y} (8 x cos (3 x y))

- 24 x^{2} sin (3 x y)

Solution steps

\frac{\partial}{\partial y} (8 x cos (3 x y))

Treat

x

as a constant

Take the constant out:

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

= 8 x \frac{\partial}{\partial y} (cos (3 x y))

Apply the chain rule:

- sin (3 x y) \frac{\partial}{\partial y} (3 x y)

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

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

= 8 x (- sin (3 x y) \cdot 3 x)

Simplify

8 x (- sin (3 x y) \cdot 3 x) : - 24 x^{2} sin (3 x y)

= - 24 x^{2} sin (3 x y)

\int \frac{( 6 x ^{2} + 7 x - 6 )}{( x ^{2} - 4 ) ( x + 2 )} d x

\int \frac{1}{1 - cos ( 2 x )} d x

\int_{0}^{4} 4 - x^{2} d x

\frac{d x}{d t} - 3 x = t

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

What is (\partial)/(\partial y)(8xcos(3xy)) ?
The answer to (\partial)/(\partial y)(8xcos(3xy)) is -24x^2sin(3xy)