What is (\partial}{\partial x}(5sin(\frac{5x)/y)) ?

The answer to (\partial}{\partial x}(5sin(\frac{5x)/y)) is (25cos((5x)/y))/(y)

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(\partial}{\partial x}(5sin(\frac{5x)/y))

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

\frac{25 cos ( \frac{5 x}{y} )}{y}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

5 cos (\frac{5 x}{y}) \frac{5}{y} : \frac{25 cos ( \frac{5 x}{y} )}{y}

= \frac{25 cos ( \frac{5 x}{y} )}{y}

What is (\partial}{\partial x}(5sin(\frac{5x)/y)) ?
The answer to (\partial}{\partial x}(5sin(\frac{5x)/y)) is (25cos((5x)/y))/(y)