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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

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

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

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