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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

- sin (4 x) \frac{\partial}{\partial x} (4 x)

= - sin (4 x) \frac{\partial}{\partial x} (4 x)

\frac{\partial}{\partial x} (4 x) = 4

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

Simplify

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

\frac{\partial}{\partial x} (e^{(x y)})

\int sin (t) e^{t} d t

\frac{12}{3 s - 5}

\frac{d ^{2}}{d x ^{2}} (\frac{6 π ^{2}}{6 - x})

n = 5 \sum \infty \frac{8 ^{n}}{9 ^{n}}

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