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

The answer to (\partial)/(\partial x)(3sin(2xy)) is 6ycos(2xy)

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(\partial)/(\partial x)(3sin(2xy))

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

6 y cos (2 x y)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= 3 cos (2 x y) \cdot 2 y

Simplify

= 6 y cos (2 x y)

x \to \infty lim (e^{8 x})

\frac{d}{d x} ((2 x^{3} + 9 x)^{5})

\int 12 x^{2} - 5 x + 4 d x

\int_{- 2}^{2} \frac{1}{x ^{2} + 4} d x

\frac{d}{d x} (e^{2 x + 5} + \frac{1}{e ^{x^{2}}})

What is (\partial)/(\partial x)(3sin(2xy)) ?
The answer to (\partial)/(\partial x)(3sin(2xy)) is 6ycos(2xy)