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

The answer to (\partial)/(\partial x)(x^2sin(3xy)) is 2xsin(3xy)+cos(3xy)*3yx^2

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

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

2 x sin (3 x y) + cos (3 x y) \cdot 3 y x^{2}

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = sin (3 x y)

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

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

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

= 2 x sin (3 x y) + cos (3 x y) \cdot 3 y x^{2}

\int sin (3 x + 1) d x

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

\int \frac{5 x ^{3}}{6 + x ^{2}} d x

\frac{d}{d x} (2 sin (2 x))

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

What is (\partial)/(\partial x)(x^2sin(3xy)) ?
The answer to (\partial)/(\partial x)(x^2sin(3xy)) is 2xsin(3xy)+cos(3xy)*3yx^2