What is (\partial)/(\partial x)(4y^3cos(3x)) ?

The answer to (\partial)/(\partial x)(4y^3cos(3x)) is -12y^3sin(3x)

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(\partial)/(\partial x)(4y^3cos(3x))

\frac{\partial}{\partial x} (4 y^{3} cos (3 x))

- 12 y^{3} sin (3 x)

Solution steps

\frac{\partial}{\partial x} (4 y^{3} cos (3 x))

Treat

y

as a constant

Take the constant out:

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

= 4 y^{3} \frac{\partial}{\partial x} (cos (3 x))

Apply the chain rule:

- sin (3 x) \frac{\partial}{\partial x} (3 x)

= - sin (3 x) \frac{\partial}{\partial x} (3 x)

\frac{\partial}{\partial x} (3 x) = 3

= 4 y^{3} (- sin (3 x) \cdot 3)

Simplify

= - 12 y^{3} sin (3 x)

h (x) = e^{x}

x \to \infty lim (1 + 2 x)

n = 1 \sum \infty (n + 1)^{2}

\int 5 e^{x} - 8 cosh (x) d x

\int 3 (x + 10)^{3} d x

What is (\partial)/(\partial x)(4y^3cos(3x)) ?
The answer to (\partial)/(\partial x)(4y^3cos(3x)) is -12y^3sin(3x)