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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

cos (3 x) \frac{\partial}{\partial x} (3 x)

= cos (3 x) \frac{\partial}{\partial x} (3 x)

\frac{\partial}{\partial x} (3 x) = 3

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

\int_{0}^{2} 6^{x} d x

x \to 0 lim (\frac{9}{x} - \frac{9}{x ^{2} + x})

x \to 1 lim (\frac{2 x - 2}{x - 1})

\int_{1}^{2} (x x - 1) d x

\int_{0}^{5} 1 + x d x

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