What is the derivative of (x-3/(3+sin(x))) ?

The derivative of (x-3/(3+sin(x))) is (3+sin(x)-cos(x)(x-3))/((3+sin(x))^2)

What is the first derivative of (x-3/(3+sin(x))) ?

The first derivative of (x-3/(3+sin(x))) is (3+sin(x)-cos(x)(x-3))/((3+sin(x))^2)

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\frac{d}{d x} (\frac{x - 3}{3 + sin ( x )})

\frac{3 + sin ( x ) - cos ( x ) ( x - 3 )}{( 3 + sin ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 3}{3 + sin ( x )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 3 ) ( 3 + sin ( x ) ) - \frac{d}{d x} ( 3 + sin ( x ) ) ( x - 3 )}{( 3 + sin ( x ) ) ^{2}}

\frac{d}{d x} (x - 3) = 1

\frac{d}{d x} (3 + sin (x)) = cos (x)

= \frac{1 \cdot ( 3 + sin ( x ) ) - cos ( x ) ( x - 3 )}{( 3 + sin ( x ) ) ^{2}}

Simplify

= \frac{3 + sin ( x ) - cos ( x ) ( x - 3 )}{( 3 + sin ( x ) ) ^{2}}

y = \frac{3}{x}, at P (0.5, 6)

\frac{d y}{d x} = - 3 x y^{3}

x \to 1 lim (x^{2} - 3)

4 y^{^{''}} - 4 y^{^{'}} + 2 y = 0

\frac{x}{x - 1}

What is the derivative of (x-3/(3+sin(x))) ?
The derivative of (x-3/(3+sin(x))) is (3+sin(x)-cos(x)(x-3))/((3+sin(x))^2)
What is the first derivative of (x-3/(3+sin(x))) ?
The first derivative of (x-3/(3+sin(x))) is (3+sin(x)-cos(x)(x-3))/((3+sin(x))^2)