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

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

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

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

y^{6} cos (5 x) \cdot 5

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

cos (5 x) \frac{\partial}{\partial x} (5 x)

= cos (5 x) \frac{\partial}{\partial x} (5 x)

\frac{\partial}{\partial x} (5 x) = 5

= y^{6} cos (5 x) \cdot 5

arctan (\frac{4}{x})

\frac{d y}{d x} + y = \frac{e ^{x}}{y}

\int_{3}^{4} e^{3 - x} d x

\int \frac{1}{6 x ^{6}} d x

ln (x), \frac{4}{x}, 1, 3

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