What is (\partial)/(\partial x)(y^4sin(5x)) ?

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

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(\partial)/(\partial x)(y^4sin(5x))

\frac{\partial}{\partial x} (y^{4} sin (5 x))

y^{4} cos (5 x) \cdot 5

Solution steps

\frac{\partial}{\partial x} (y^{4} sin (5 x))

Treat

y

as a constant

Take the constant out:

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

= y^{4} \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^{4} cos (5 x) \cdot 5

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\int cos^{2} (x) sec^{2} (x) d x

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