What is (\partial)/(\partial y)(7xsin(9x^2y)) ?

The answer to (\partial)/(\partial y)(7xsin(9x^2y)) is 63x^3cos(9x^2y)

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(\partial)/(\partial y)(7xsin(9x^2y))

\frac{\partial}{\partial y} (7 x sin (9 x^{2} y))

63 x^{3} cos (9 x^{2} y)

Solution steps

\frac{\partial}{\partial y} (7 x sin (9 x^{2} y))

Treat

x

as a constant

Take the constant out:

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

= 7 x \frac{\partial}{\partial y} (sin (9 x^{2} y))

Apply the chain rule:

cos (9 x^{2} y) \frac{\partial}{\partial y} (9 x^{2} y)

= cos (9 x^{2} y) \frac{\partial}{\partial y} (9 x^{2} y)

\frac{\partial}{\partial y} (9 x^{2} y) = 9 x^{2}

= 7 x cos (9 x^{2} y) \cdot 9 x^{2}

Simplify

7 x cos (9 x^{2} y) \cdot 9 x^{2} : 63 x^{3} cos (9 x^{2} y)

= 63 x^{3} cos (9 x^{2} y)

x \to - \infty lim (x e^{- x + 2})

\frac{\partial}{\partial x} (ln (x + 3 y + 4 z))

\int \frac{x ^{2}}{( 3 x + 1 ) ^{3}} d x

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

\frac{d}{d x} (x cos (π x) + 1)

What is (\partial)/(\partial y)(7xsin(9x^2y)) ?
The answer to (\partial)/(\partial y)(7xsin(9x^2y)) is 63x^3cos(9x^2y)