What is (\partial)/(\partial x)((2y)/(y+cos(x))) ?

The answer to (\partial)/(\partial x)((2y)/(y+cos(x))) is (2ysin(x))/((y+cos(x))^2)

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(\partial)/(\partial x)((2y)/(y+cos(x)))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= 2 y \frac{\partial}{\partial x} (\frac{1}{y + cos ( x )})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (y + cos (x)) = - sin (x)

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

Simplify

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

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

\int \frac{x + 2}{( x + 1 ) ^{2}} d x

\int_{0}^{10} 9800 π (10 - y) d y

f (x) = \frac{- x ^{2}}{200}

\frac{d}{d x} ((x^{2} + 1) (x + 5 + \frac{1}{x}))

y = 4 x^{2}, y = 24

What is (\partial)/(\partial x)((2y)/(y+cos(x))) ?
The answer to (\partial)/(\partial x)((2y)/(y+cos(x))) is (2ysin(x))/((y+cos(x))^2)