Solve \frac{\partial}{\partial x}\left[\frac{2 y}{y+\

Calcule

\frac{\partial}{\partial x} (\frac{2 y}{y + cos ( x )})

Use a regra de diferencia \overset{c}{¸} \overset{a}{˜} o \frac{\partial}{\partial x} (\frac{f ( x )}{g ( x )}) = \frac{\frac{\partial}{\partial x} ( f ( x )) \times g ( x ) - f ( x ) \times \frac{\partial}{\partial x} ( g ( x ) )}{( g ( x ) ) ^{2}}

\frac{\frac{\partial}{\partial x} ( 2 y ) ( y + cos ( x ) ) - 2 y \times \frac{\partial}{\partial x} ( y + cos ( x ) )}{( y + cos ( x ) ) ^{2}}

Use \frac{\partial}{\partial x} (c) = 0 para encontrar derivada

\frac{0 \times ( y + cos ( x ) ) - 2 y \times \frac{\partial}{\partial x} ( y + cos ( x ) )}{( y + cos ( x ) ) ^{2}}

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\frac{0 \times ( y + cos ( x ) ) - 2 y ( - sin ( x ) )}{( y + cos ( x ) ) ^{2}}

Qualquer expressão multiplicada por 0 é igual a 0

\frac{0 - 2 y ( - sin ( x ) )}{( y + cos ( x ) ) ^{2}}

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\frac{0 - ( - 2 y sin ( x ) )}{( y + cos ( x ) ) ^{2}}

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\frac{2 y sin ( x )}{( y + cos ( x ) ) ^{2}}

Solution

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\frac{2 y sin ( x )}{y ^{2} + 2 y cos ( x ) + cos ^{2} ( x )}

\frac{\partial}{\partial x}\left[\frac{2 y}{y+\cos x}\right]