What is (\partial)/(\partial x)(30y^4sin(2x)) ?

The answer to (\partial)/(\partial x)(30y^4sin(2x)) is 60y^4cos(2x)

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(\partial)/(\partial x)(30y^4sin(2x))

\frac{\partial}{\partial x} (30 y^{4} sin (2 x))

60 y^{4} cos (2 x)

Solution steps

\frac{\partial}{\partial x} (30 y^{4} sin (2 x))

Treat

y

as a constant

Take the constant out:

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

= 30 y^{4} \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

= 30 y^{4} cos (2 x) \cdot 2

Simplify

= 60 y^{4} cos (2 x)

(x - 4) ln (4 - x)

\frac{d}{d x} (x sin (4 x))

f (x) = cos (\frac{π x}{2}), at x = 0.4

\int 30 e^{- x} d x

\frac{\partial}{\partial x} (9 x y)

What is (\partial)/(\partial x)(30y^4sin(2x)) ?
The answer to (\partial)/(\partial x)(30y^4sin(2x)) is 60y^4cos(2x)