What is (\partial)/(\partial x)(4ysin(2x)) ?

The answer to (\partial)/(\partial x)(4ysin(2x)) is 8ycos(2x)

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(\partial)/(\partial x)(4ysin(2x))

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

8 y cos (2 x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= 4 y \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

= 4 y cos (2 x) \cdot 2

Simplify

= 8 y cos (2 x)

e^{y} y^{^{'}} = e^{y} + 7 x

\int x sin (2 x^{2}) d x

\frac{d}{d x} (5 x^{7} sin (x))

f (x) = \frac{cot ( x )}{sin ( x )}

ln (x + 1)

What is (\partial)/(\partial x)(4ysin(2x)) ?
The answer to (\partial)/(\partial x)(4ysin(2x)) is 8ycos(2x)