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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

- sin (3 x) \frac{\partial}{\partial x} (3 x)

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

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

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

Simplify

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

\int \frac{3 x ^{2} + 2}{( x ^{3} + 2 x + 3 ) ^{5}} d x

y^{^{'}} = \frac{x ^{2} + y ^{2}}{x \cdot y}

\frac{d}{d x} (cos (10 x))

x y^{^{'}} + y^{^{'}} - (x + 1) cos (x) + y = 0

\frac{d}{d x} ((e^{- x} + e^{x})^{3})

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