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

The answer to (\partial)/(\partial x)((5y^4)cos(5x)) is -25y^4sin(5x)

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

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

- 25 y^{4} sin (5 x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

- sin (5 x) \frac{\partial}{\partial x} (5 x)

= - sin (5 x) \frac{\partial}{\partial x} (5 x)

\frac{\partial}{\partial x} (5 x) = 5

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

Simplify

= - 25 y^{4} sin (5 x)

d er i v a t i v e h (t) = (t + 2)^{\frac{2}{3}} (2 t^{2} - 3)^{3}

\frac{d y}{d t} = (- csc (t) cot (t)) e^{- c s c (t)}

x \to \infty lim (- 3 x^{3})

x \to 0 - lim (1 - x^{2})

x \to 0 lim ((1 - 4 x)^{\frac{7}{x}})

What is (\partial)/(\partial x)((5y^4)cos(5x)) ?
The answer to (\partial)/(\partial x)((5y^4)cos(5x)) is -25y^4sin(5x)