What is (\partial)/(\partial x)(y^3sin(5x)) ?

The answer to (\partial)/(\partial x)(y^3sin(5x)) is y^3cos(5x)*5

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(\partial)/(\partial x)(y^3sin(5x))

\frac{\partial}{\partial x} (y^{3} sin (5 x))

y^{3} cos (5 x) \cdot 5

Solution steps

\frac{\partial}{\partial x} (y^{3} sin (5 x))

Treat

y

as a constant

Take the constant out:

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

= y^{3} \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^{3} cos (5 x) \cdot 5

\frac{z}{z + \frac{d}{z}}

ln (4 x)

\frac{\partial}{\partial y} (2 x - 2 x y)

f^{^{'}} (x) = x^{\frac{1}{3}} (2 x - 1) (x + 1)

What is (\partial)/(\partial x)(y^3sin(5x)) ?
The answer to (\partial)/(\partial x)(y^3sin(5x)) is y^3cos(5x)*5