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

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

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

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

2 cos (x y^{2}) y^{2}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= 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}

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

\frac{\partial}{\partial x} (\frac{5 x}{e ^{x}})

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

\frac{d}{d x} (- \frac{3}{4} x^{- \frac{2}{3}})

\int \frac{7}{4 x ^{3}} d x

t y^{^{'}} - y = \frac{- t ^{3}}{y ^{2}}, y (1) = 2

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