What is (\partial)/(\partial x)(5y^4cos(4x)) ?

The answer to (\partial)/(\partial x)(5y^4cos(4x)) is -20y^4sin(4x)

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(\partial)/(\partial x)(5y^4cos(4x))

\frac{\partial}{\partial x} (5 y^{4} cos (4 x))

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

Solution steps

\frac{\partial}{\partial x} (5 y^{4} cos (4 x))

Treat

y

as a constant

Take the constant out:

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

= 5 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

= 5 y^{4} (- sin (4 x) \cdot 4)

Simplify

= - 20 y^{4} sin (4 x)

\int sin^{\frac{1}{2}} (x) cos (x) d x

x^{3} \frac{d y}{d x} + 3 x^{2} y = x

(\frac{2}{5} x)^{3}

\frac{\partial}{\partial x} (- 2 x^{2} + 4 y^{2} + 3 z^{2} + 43)

\frac{\partial}{\partial y} (2 x + y e^{x})

What is (\partial)/(\partial x)(5y^4cos(4x)) ?
The answer to (\partial)/(\partial x)(5y^4cos(4x)) is -20y^4sin(4x)