What is (\partial)/(\partial x)(-5y^2sin(xy^2)) ?

The answer to (\partial)/(\partial x)(-5y^2sin(xy^2)) is -5y^4cos(y^2x)

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(\partial)/(\partial x)(-5y^2sin(xy^2))

\frac{\partial}{\partial x} (- 5 y^{2} sin (x y^{2}))

- 5 y^{4} cos (y^{2} x)

Solution steps

\frac{\partial}{\partial x} (- 5 y^{2} sin (x y^{2}))

Treat

y

as a constant

Take the constant out:

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

= - 5 y^{2} \frac{\partial}{\partial x} (sin (x y^{2}))

Apply the chain rule:

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

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

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

= - 5 y^{2} cos (x y^{2}) y^{2}

Simplify

- 5 y^{2} cos (x y^{2}) y^{2} : - 5 y^{4} cos (y^{2} x)

= - 5 y^{4} cos (y^{2} x)

\frac{\partial}{\partial y} (20 (y - x^{2}))

x \to 1 lim (\frac{x ^{2} + 1}{x + 5})

\int \frac{( x ^{3} - x )}{x} d x

(x + y)^{2} d x + (2 x y + x^{2} - 6) d y = 0, y (1) = 1

\frac{d}{d x} (\frac{- 6}{x})

What is (\partial)/(\partial x)(-5y^2sin(xy^2)) ?
The answer to (\partial)/(\partial x)(-5y^2sin(xy^2)) is -5y^4cos(y^2x)