What is (\partial)/(\partial x)(7x(sin(3x^2y))) ?

The answer to (\partial)/(\partial x)(7x(sin(3x^2y))) is 7(sin(3x^2y)+6x^2ycos(3x^2y))

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(\partial)/(\partial x)(7x(sin(3x^2y)))

\frac{\partial}{\partial x} (7 x (sin (3 x^{2} y)))

7 (sin (3 x^{2} y) + 6 x^{2} y cos (3 x^{2} y))

Solution steps

\frac{\partial}{\partial x} (7 x (sin (3 x^{2} y)))

Treat

y

as a constant

Take the constant out:

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

= 7 \frac{\partial}{\partial x} (x sin (3 x^{2} y))

Apply the Product Rule:

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

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

= 7 (\frac{\partial}{\partial x} (x) sin (3 x^{2} y) + \frac{\partial}{\partial x} (sin (3 x^{2} y)) x)

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (sin (3 x^{2} y)) = cos (3 x^{2} y) \cdot 6 y x

= 7 (1 \cdot sin (3 x^{2} y) + cos (3 x^{2} y) \cdot 6 y xx)

Simplify

7 (1 \cdot sin (3 x^{2} y) + cos (3 x^{2} y) \cdot 6 y xx) : 7 (sin (3 x^{2} y) + 6 x^{2} y cos (3 x^{2} y))

= 7 (sin (3 x^{2} y) + 6 x^{2} y cos (3 x^{2} y))

\int - \frac{1}{6 - x} d x

x \to \infty lim (10000)

\int_{0}^{\frac{π}{8}} sin (8 x) d x

\frac{d ^{2}}{d x ^{2}} (2 x^{\frac{3}{2}})

x \to - 41 lim (39 + x)

What is (\partial)/(\partial x)(7x(sin(3x^2y))) ?
The answer to (\partial)/(\partial x)(7x(sin(3x^2y))) is 7(sin(3x^2y)+6x^2ycos(3x^2y))