What is (\partial)/(\partial y)(-2y^4sin(2x)) ?

The answer to (\partial)/(\partial y)(-2y^4sin(2x)) is -8y^3sin(2x)

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(\partial)/(\partial y)(-2y^4sin(2x))

\frac{\partial}{\partial y} (- 2 y^{4} sin (2 x))

- 8 y^{3} sin (2 x)

Solution steps

\frac{\partial}{\partial y} (- 2 y^{4} sin (2 x))

Treat

x

as a constant

Take the constant out:

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

= - 2 sin (2 x) \frac{\partial}{\partial y} (y^{4})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - 2 sin (2 x) \cdot 4 y^{4 - 1}

Simplify

= - 8 y^{3} sin (2 x)

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

- 2 x^{2} - 4 x + 1

(\frac{10}{x})^{^{'}}

x \to 8 - lim (\frac{x - 8}{x - 8})

x \to 12 lim (\frac{x - 12}{x ^{2} - 144})

What is (\partial)/(\partial y)(-2y^4sin(2x)) ?
The answer to (\partial)/(\partial y)(-2y^4sin(2x)) is -8y^3sin(2x)