What is the derivative of sin(x/(1+y)) ?

The derivative of sin(x/(1+y)) is (cos(x/(1+y))(1+y-x\frac{dy)/(dx))}{(1+y)^2}

What is the first derivative of sin(x/(1+y)) ?

The first derivative of sin(x/(1+y)) is (cos(x/(1+y))(1+y-x\frac{dy)/(dx))}{(1+y)^2}

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\frac{d}{d x} (sin (\frac{x}{1 + y}))

\frac{cos ( \frac{x}{1 + y} ) ( 1 + y - x \frac{d y}{d x} )}{( 1 + y ) ^{2}}

Solution steps

\frac{d}{d x} (sin (\frac{x}{1 + y}))

Apply the chain rule:

cos (\frac{x}{1 + y}) \frac{d}{d x} (\frac{x}{1 + y})

= cos (\frac{x}{1 + y}) \frac{d}{d x} (\frac{x}{1 + y})

\frac{d}{d x} (\frac{x}{1 + y}) = \frac{1 + y - x \frac{d y}{d x}}{( 1 + y ) ^{2}}

= cos (\frac{x}{1 + y}) \frac{1 + y - x \frac{d y}{d x}}{( 1 + y ) ^{2}}

Multiply fractions:

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

= \frac{cos ( \frac{x}{1 + y} ) ( 1 + y - x \frac{d y}{d x} )}{( 1 + y ) ^{2}}

What is the derivative of sin(x/(1+y)) ?
The derivative of sin(x/(1+y)) is (cos(x/(1+y))(1+y-x\frac{dy)/(dx))}{(1+y)^2}
What is the first derivative of sin(x/(1+y)) ?
The first derivative of sin(x/(1+y)) is (cos(x/(1+y))(1+y-x\frac{dy)/(dx))}{(1+y)^2}