What is (\partial)/(\partial y)(y^6sin(4x)) ?

The answer to (\partial)/(\partial y)(y^6sin(4x)) is 6y^5sin(4x)

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(\partial)/(\partial y)(y^6sin(4x))

\frac{\partial}{\partial y} (y^{6} sin (4 x))

6 y^{5} sin (4 x)

Solution steps

\frac{\partial}{\partial y} (y^{6} sin (4 x))

Treat

x

as a constant

Take the constant out:

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

= sin (4 x) \frac{\partial}{\partial y} (y^{6})

Apply the Power Rule:

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

= sin (4 x) \cdot 6 y^{6 - 1}

Simplify

= 6 y^{5} sin (4 x)

\int_{0}^{1} 1 + x d x

\int_{0}^{1} π (1 - x^{2})^{2} d x

(3 + 4 x) + (5 y - 1) \frac{d y}{d x} = 0

f (x) = x^{2} + 5 x - 2, at x = 4

x \to 0 lim (2 x^{2} + 3 x)

What is (\partial)/(\partial y)(y^6sin(4x)) ?
The answer to (\partial)/(\partial y)(y^6sin(4x)) is 6y^5sin(4x)