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

The answer to (\partial)/(\partial x)(x^3sin(5y)) is 3x^2sin(5y)

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

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

3 x^{2} sin (5 y)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= sin (5 y) \cdot 3 x^{3 - 1}

Simplify

= 3 x^{2} sin (5 y)

2 e^{- t} sin (2 t)

(1 + t e^{- t})^{3}

\int \frac{2 x}{x - 1} d x

t \frac{d y}{d t} + 34 y = \frac{1}{t}

f (x) = x - 1, at x = 5

What is (\partial)/(\partial x)(x^3sin(5y)) ?
The answer to (\partial)/(\partial x)(x^3sin(5y)) is 3x^2sin(5y)