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

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

Popular >

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

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

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

Solution steps

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

Treat

y

as a constant

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}

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

Multiply fractions:

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

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

\frac{\partial}{\partial x} ((3 x y - 1) e^{- x y})

\int \frac{2}{3 x + 1} d x

\int_{4}^{8} ln (x^{2}) d x

\int_{0}^{\frac{π}{3}} x sec^{2} (x) d x

2 x, x^{2}

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