What is (\partial)/(\partial x)(-5y^3sin(5x)) ?

The answer to (\partial)/(\partial x)(-5y^3sin(5x)) is -25y^3cos(5x)

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(\partial)/(\partial x)(-5y^3sin(5x))

\frac{\partial}{\partial x} (- 5 y^{3} sin (5 x))

- 25 y^{3} cos (5 x)

Solution steps

\frac{\partial}{\partial x} (- 5 y^{3} sin (5 x))

Treat

y

as a constant

Take the constant out:

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

= - 5 y^{3} \frac{\partial}{\partial x} (sin (5 x))

Apply the chain rule:

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

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

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

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

Simplify

= - 25 y^{3} cos (5 x)

y = \frac{2}{x}, y = 8 x, y = \frac{1}{8} x

\int_{2}^{\infty} \frac{1}{ln ( x )} d x

x \to \infty lim (- \frac{1}{2} e^{- x^{2}})

\int_{1}^{2} cos (\frac{π x}{3}) d x

\int_{1}^{2} \frac{1}{4 - x ^{2}} d x

What is (\partial)/(\partial x)(-5y^3sin(5x)) ?
The answer to (\partial)/(\partial x)(-5y^3sin(5x)) is -25y^3cos(5x)