What is (\partial)/(\partial y)(-5y^6sin(5x)) ?

The answer to (\partial)/(\partial y)(-5y^6sin(5x)) is -30y^5sin(5x)

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(\partial)/(\partial y)(-5y^6sin(5x))

\frac{\partial}{\partial y} (- 5 y^{6} sin (5 x))

- 30 y^{5} sin (5 x)

Solution steps

\frac{\partial}{\partial y} (- 5 y^{6} sin (5 x))

Treat

x

as a constant

Take the constant out:

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

= - 5 sin (5 x) \frac{\partial}{\partial y} (y^{6})

Apply the Power Rule:

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

= - 5 sin (5 x) \cdot 6 y^{6 - 1}

Simplify

= - 30 y^{5} sin (5 x)

\frac{d}{d x} (50 (80 - x)^{2})

x \to 0 lim (\frac{1}{2} + \frac{x}{2 ∣ x ∣})

x \to 0 lim (\frac{x ^{2} + 4 x}{x})

f (x) = x e^{x} + e^{x}

\frac{- 3 s - 20}{s ^{2} + 256}

What is (\partial)/(\partial y)(-5y^6sin(5x)) ?
The answer to (\partial)/(\partial y)(-5y^6sin(5x)) is -30y^5sin(5x)