What is the derivative of (6x)/(7-cot(x)) ?

The derivative of (6x)/(7-cot(x)) is (6(7-cot(x)-xcsc^2(x)))/((7-cot(x))^2)

What is the first derivative of (6x)/(7-cot(x)) ?

The first derivative of (6x)/(7-cot(x)) is (6(7-cot(x)-xcsc^2(x)))/((7-cot(x))^2)

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derivative of

\frac{6 x}{7 - cot ( x )}

\frac{6 ( 7 - cot ( x ) - x csc ^{2} ( x ) )}{( 7 - cot ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{6 x}{7 - cot ( x )})

Take the constant out:

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

= 6 \frac{d}{d x} (\frac{x}{7 - cot ( x )})

Apply the Quotient Rule:

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

= 6 \cdot \frac{\frac{d x}{d x} ( 7 - cot ( x ) ) - \frac{d}{d x} ( 7 - cot ( x ) ) x}{( 7 - cot ( x ) ) ^{2}}

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

\frac{d}{d x} (7 - cot (x)) = csc^{2} (x)

= 6 \cdot \frac{1 \cdot ( 7 - cot ( x ) ) - csc ^{2} ( x ) x}{( 7 - cot ( x ) ) ^{2}}

Simplify

6 \cdot \frac{1 \cdot ( 7 - cot ( x ) ) - csc ^{2} ( x ) x}{( 7 - cot ( x ) ) ^{2}} : \frac{6 ( 7 - cot ( x ) - x csc ^{2} ( x ) )}{( 7 - cot ( x ) ) ^{2}}

= \frac{6 ( 7 - cot ( x ) - x csc ^{2} ( x ) )}{( 7 - cot ( x ) ) ^{2}}

x \to \infty lim (\frac{5}{0})

y^{^{''}} - y^{^{'}} - 6 y = 0, y (0) = 1, y^{^{'}} (0) = 1

\frac{d y}{d x} = 4 y + 3 e^{8 x} (x + 1)

\int \frac{r}{1 + r ^{2}} d r

\int \frac{e ^{x}}{1 + 49 e ^{2 x}} d x

What is the derivative of (6x)/(7-cot(x)) ?
The derivative of (6x)/(7-cot(x)) is (6(7-cot(x)-xcsc^2(x)))/((7-cot(x))^2)
What is the first derivative of (6x)/(7-cot(x)) ?
The first derivative of (6x)/(7-cot(x)) is (6(7-cot(x)-xcsc^2(x)))/((7-cot(x))^2)