What is (\partial)/(\partial x)(y^5sin(2x)) ?

The answer to (\partial)/(\partial x)(y^5sin(2x)) is y^5cos(2x)*2

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(\partial)/(\partial x)(y^5sin(2x))

\frac{\partial}{\partial x} (y^{5} sin (2 x))

y^{5} cos (2 x) \cdot 2

Solution steps

\frac{\partial}{\partial x} (y^{5} sin (2 x))

Treat

y

as a constant

Take the constant out:

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

= y^{5} \frac{\partial}{\partial x} (sin (2 x))

Apply the chain rule:

cos (2 x) \frac{\partial}{\partial x} (2 x)

= cos (2 x) \frac{\partial}{\partial x} (2 x)

\frac{\partial}{\partial x} (2 x) = 2

= y^{5} cos (2 x) \cdot 2

4 - x^{2}, x^{2} - 2 x

y^{^{''}} - 2 y^{^{'}} + y = t e^{t} + 4

y^{^{''}} + 36 y = sec^{2} (6 x)

y^{^{'}} = 3 x^{2} (1 + y^{2})

\frac{d}{d x} (\frac{x - 4}{x} + ln (\frac{x}{4}))

What is (\partial)/(\partial x)(y^5sin(2x)) ?
The answer to (\partial)/(\partial x)(y^5sin(2x)) is y^5cos(2x)*2