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

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

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

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

4 y^{3} sin (3 x)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= sin (3 x) \cdot 4 y^{4 - 1}

Simplify

= 4 y^{3} sin (3 x)

\int \frac{1}{x ^{2} + 2 x + 6} d x

\int (e^{2 t} + \frac{1}{( t + 1 ) ^{2}}) d t

\frac{s - 3}{s ^{2} + 10 s + 9}

x \to 4 lim (2 x + 1)

\int \frac{1}{- u ^{2} + 1} d u

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