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

The answer to (\partial)/(\partial x)(-4y^5sin(4x)) is -16y^5cos(4x)

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(\partial)/(\partial x)(-4y^5sin(4x))

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

- 16 y^{5} cos (4 x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

= - 16 y^{5} cos (4 x)

\frac{\partial}{\partial x} (7 x^{5} y^{7} + 3 x^{8} y^{6})

f (x) = 4 (x - \frac{1}{x})^{4}, at x = 2

n = 1 \sum \infty \frac{1}{6 n}

4 x - x

\frac{2}{( s ^{2} + 2 ) ( s ^{2} + 1 )}

What is (\partial)/(\partial x)(-4y^5sin(4x)) ?
The answer to (\partial)/(\partial x)(-4y^5sin(4x)) is -16y^5cos(4x)