What is (\partial)/(\partial x)(4y^3cos(5x)) ?

The answer to (\partial)/(\partial x)(4y^3cos(5x)) is -20y^3sin(5x)

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(\partial)/(\partial x)(4y^3cos(5x))

\frac{\partial}{\partial x} (4 y^{3} cos (5 x))

- 20 y^{3} sin (5 x)

Solution steps

\frac{\partial}{\partial x} (4 y^{3} cos (5 x))

Treat

y

as a constant

Take the constant out:

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

= 4 y^{3} \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

= 4 y^{3} (- sin (5 x) \cdot 5)

Simplify

= - 20 y^{3} sin (5 x)

n = 0 \sum \infty \frac{2}{3 ^{n - 1}}

\int - 3 x^{2} d x

\frac{\partial}{\partial z} (\frac{x ^{2}}{y} - x z)

\int \frac{x}{4 + x ^{4}} d x

\frac{\partial}{\partial y} (\frac{7}{x ^{2} + y ^{2}})

What is (\partial)/(\partial x)(4y^3cos(5x)) ?
The answer to (\partial)/(\partial x)(4y^3cos(5x)) is -20y^3sin(5x)