What is (\partial)/(\partial x)(4y^3sin(5x)) ?

The answer to (\partial)/(\partial x)(4y^3sin(5x)) is 20y^3cos(5x)

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(\partial)/(\partial x)(4y^3sin(5x))

\frac{\partial}{\partial x} (4 y^{3} sin (5 x))

20 y^{3} cos (5 x)

Solution steps

\frac{\partial}{\partial x} (4 y^{3} sin (5 x))

Treat

y

as a constant

Take the constant out:

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

= 4 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

= 4 y^{3} cos (5 x) \cdot 5

Simplify

= 20 y^{3} cos (5 x)

\frac{s ^{2} - s + 1}{( s + 1 ) ^{2}}

x^{2} - 5, 4

x y^{^{'}} - y = 2 x^{2}

\int_{0}^{1} 2 π (x + 10) x^{2} d x

f (x) = 12 x^{2} - 48 x

What is (\partial)/(\partial x)(4y^3sin(5x)) ?
The answer to (\partial)/(\partial x)(4y^3sin(5x)) is 20y^3cos(5x)