What is (\partial}{\partial x}(sin(\frac{3x)/y)) ?

The answer to (\partial}{\partial x}(sin(\frac{3x)/y)) is (3cos((3x)/y))/(y)

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(\partial}{\partial x}(sin(\frac{3x)/y))

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

\frac{3 cos ( \frac{3 x}{y} )}{y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= cos (\frac{3 x}{y}) \frac{3}{y}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 cos ( \frac{3 x}{y} )}{y}

\frac{d}{d x} (e^{(x^{2})})

\int \frac{x + 4}{x ^{2} + 8 x} d x

x y^{^{'}} + y = 2 x

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

x \to 0 lim (\frac{3}{1 + e ^{\frac{1}{x}}})

What is (\partial}{\partial x}(sin(\frac{3x)/y)) ?
The answer to (\partial}{\partial x}(sin(\frac{3x)/y)) is (3cos((3x)/y))/(y)