What is the derivative of (2x/(5-tan(x))) ?

The derivative of (2x/(5-tan(x))) is (2(5-tan(x)+xsec^2(x)))/((5-tan(x))^2)

What is the first derivative of (2x/(5-tan(x))) ?

The first derivative of (2x/(5-tan(x))) is (2(5-tan(x)+xsec^2(x)))/((5-tan(x))^2)

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\frac{d}{d x} (\frac{2 x}{5 - tan ( x )})

\frac{2 ( 5 - tan ( x ) + x sec ^{2} ( x ) )}{( 5 - tan ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x}{5 - tan ( x )})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{x}{5 - tan ( 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} ( 5 - tan ( x ) ) - \frac{d}{d x} ( 5 - tan ( x ) ) x}{( 5 - tan ( x ) ) ^{2}}

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

\frac{d}{d x} (5 - tan (x)) = - sec^{2} (x)

= 2 \cdot \frac{1 \cdot ( 5 - tan ( x ) ) - ( - sec ^{2} ( x ) ) x}{( 5 - tan ( x ) ) ^{2}}

Simplify

2 \cdot \frac{1 \cdot ( 5 - tan ( x ) ) - ( - sec ^{2} ( x ) ) x}{( 5 - tan ( x ) ) ^{2}} : \frac{2 ( 5 - tan ( x ) + x sec ^{2} ( x ) )}{( 5 - tan ( x ) ) ^{2}}

= \frac{2 ( 5 - tan ( x ) + x sec ^{2} ( x ) )}{( 5 - tan ( x ) ) ^{2}}

\frac{d}{d x} (\frac{2 x + 5}{3 x - 1})

\int (6 x^{5} - 4 x^{3} + \frac{1}{x}) d x

4 e (cos (x) - x sin (x))

x \to 4 lim (\frac{6}{x - 4})

x \to 3 lim (2 x + ∣ x + 3 ∣)

What is the derivative of (2x/(5-tan(x))) ?
The derivative of (2x/(5-tan(x))) is (2(5-tan(x)+xsec^2(x)))/((5-tan(x))^2)
What is the first derivative of (2x/(5-tan(x))) ?
The first derivative of (2x/(5-tan(x))) is (2(5-tan(x)+xsec^2(x)))/((5-tan(x))^2)