What is the derivative of f(x)=(2x)/(sin(x)+cos(x)) ?

The derivative of f(x)=(2x)/(sin(x)+cos(x)) is (2(sin(x)+cos(x)-x(cos(x)-sin(x))))/(1+sin(2x))

What is the first derivative of f(x)=(2x)/(sin(x)+cos(x)) ?

The first derivative of f(x)=(2x)/(sin(x)+cos(x)) is (2(sin(x)+cos(x)-x(cos(x)-sin(x))))/(1+sin(2x))

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derivative of

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

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

Solution steps

\frac{d}{d x} (\frac{2 x}{sin ( x ) + cos ( x )})

Take the constant out:

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

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 2 \cdot \frac{\frac{d x}{d x} ( sin ( x ) + cos ( x ) ) - \frac{d}{d x} ( sin ( x ) + cos ( x ) ) x}{( sin ( x ) + cos ( x ) ) ^{2}}

\frac{d x}{d x} = 1

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

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

Simplify

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

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

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

x \to 2 lim (\frac{3}{x})

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

\int 3 x^{2} y + e^{x} sin (y) d x

y^{^{'}} + \frac{( x - 2 )}{x - 1} y = 0

What is the derivative of f(x)=(2x)/(sin(x)+cos(x)) ?
The derivative of f(x)=(2x)/(sin(x)+cos(x)) is (2(sin(x)+cos(x)-x(cos(x)-sin(x))))/(1+sin(2x))
What is the first derivative of f(x)=(2x)/(sin(x)+cos(x)) ?
The first derivative of f(x)=(2x)/(sin(x)+cos(x)) is (2(sin(x)+cos(x)-x(cos(x)-sin(x))))/(1+sin(2x))