What is (\partial)/(\partial y)(x^2cos(e^{xy})) ?

The answer to (\partial)/(\partial y)(x^2cos(e^{xy})) is -e^{xy}x^3sin(e^{xy})

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(\partial)/(\partial y)(x^2cos(e^{xy}))

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

- e^{x y} x^{3} sin (e^{x y})

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

- sin (e^{x y}) \frac{\partial}{\partial y} (e^{x y})

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

\frac{\partial}{\partial y} (e^{x y}) = e^{x y} x

= x^{2} (- sin (e^{x y}) e^{x y} x)

Simplify

x^{2} (- sin (e^{x y}) e^{x y} x) : - e^{x y} x^{3} sin (e^{x y})

= - e^{x y} x^{3} sin (e^{x y})

y^{^{''}} + 6 y^{^{'}} + 9 y = - x e^{4 x}

\int \frac{8 x}{x ^{2} + x + 1} d x

x \to - 2 lim (x^{2} - 1)

\int (w + rs - \frac{1}{c} e^{(r - p) t}) d t

\frac{d}{d x} ((sin (3 x))^{l n (x)})

What is (\partial)/(\partial y)(x^2cos(e^{xy})) ?
The answer to (\partial)/(\partial y)(x^2cos(e^{xy})) is -e^{xy}x^3sin(e^{xy})