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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

\frac{2 x ^{4} + 3 x ^{2} - 1}{x ^{2}}

\frac{d}{d x} (x^{4} (x - 3)^{3})

\int 8 x^{5} e^{5 x^{6}} d x

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + y = 0

y = 9 ln (5 x), y = 11, [2, 4]

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