What is the derivative of (2x/(7-tan(x))) ?

The derivative of (2x/(7-tan(x))) is (2(7-tan(x)+xsec^2(x)))/((7-tan(x))^2)

What is the first derivative of (2x/(7-tan(x))) ?

The first derivative of (2x/(7-tan(x))) is (2(7-tan(x)+xsec^2(x)))/((7-tan(x))^2)

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\frac{d}{d x} (\frac{2 x}{7 - tan ( x )})

\frac{2 ( 7 - tan ( x ) + x sec ^{2} ( x ) )}{( 7 - tan ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x}{7 - tan ( x )})

Take the constant out:

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

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

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

\frac{d}{d x} (7 - tan (x)) = - sec^{2} (x)

= 2 \cdot \frac{1 \cdot ( 7 - tan ( x ) ) - ( - sec ^{2} ( x ) ) x}{( 7 - tan ( x ) ) ^{2}}

Simplify

2 \cdot \frac{1 \cdot ( 7 - tan ( x ) ) - ( - sec ^{2} ( x ) ) x}{( 7 - tan ( x ) ) ^{2}} : \frac{2 ( 7 - tan ( x ) + x sec ^{2} ( x ) )}{( 7 - tan ( x ) ) ^{2}}

= \frac{2 ( 7 - tan ( x ) + x sec ^{2} ( x ) )}{( 7 - tan ( x ) ) ^{2}}

\int_{a}^{2 a} a - \frac{a ^{3}}{x ^{2}} d x

7 ln (sec (x) + tan (x))

x \to 7 lim (c x + 8)

θ \to 0 lim (cot (θ))

\frac{\partial}{\partial y} (x^{3} y^{5} + 2 x^{4} y)

What is the derivative of (2x/(7-tan(x))) ?
The derivative of (2x/(7-tan(x))) is (2(7-tan(x)+xsec^2(x)))/((7-tan(x))^2)
What is the first derivative of (2x/(7-tan(x))) ?
The first derivative of (2x/(7-tan(x))) is (2(7-tan(x)+xsec^2(x)))/((7-tan(x))^2)