What is (\partial)/(\partial x)(y^6cos(4x)*4) ?

The answer to (\partial)/(\partial x)(y^6cos(4x)*4) is -16y^6sin(4x)

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(\partial)/(\partial x)(y^6cos(4x)*4)

\frac{\partial}{\partial x} (y^{6} cos (4 x) \cdot 4)

- 16 y^{6} sin (4 x)

Solution steps

\frac{\partial}{\partial x} (y^{6} cos (4 x) \cdot 4)

Treat

y

as a constant

Take the constant out:

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

= y^{6} \cdot 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^{6} \cdot 4 (- sin (4 x) \cdot 4)

Simplify

= - 16 y^{6} sin (4 x)

n = 1 \sum \infty \frac{9}{10 0 ^{n}}

x \to 0 lim (g (x))

\frac{\partial}{\partial x} (2 x y)

\int e^{7 x} sin (7 x) d x

\frac{d y}{d x} = x^{6} (y - 2), y (0) = 6

What is (\partial)/(\partial x)(y^6cos(4x)*4) ?
The answer to (\partial)/(\partial x)(y^6cos(4x)*4) is -16y^6sin(4x)