What is the derivative of f(x)=(2x)/(3-tan(x)) ?

The derivative of f(x)=(2x)/(3-tan(x)) is (2(3-tan(x)+xsec^2(x)))/((3-tan(x))^2)

What is the first derivative of f(x)=(2x)/(3-tan(x)) ?

The first derivative of f(x)=(2x)/(3-tan(x)) is (2(3-tan(x)+xsec^2(x)))/((3-tan(x))^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = \frac{2 x}{3 - tan ( x )}

\frac{2 ( 3 - tan ( x ) + x sec ^{2} ( x ) )}{( 3 - tan ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x}{3 - tan ( x )})

Take the constant out:

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

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

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

\frac{d}{d x} (3 - tan (x)) = - sec^{2} (x)

= 2 \cdot \frac{1 \cdot ( 3 - tan ( x ) ) - ( - sec ^{2} ( x ) ) x}{( 3 - tan ( x ) ) ^{2}}

Simplify

2 \cdot \frac{1 \cdot ( 3 - tan ( x ) ) - ( - sec ^{2} ( x ) ) x}{( 3 - tan ( x ) ) ^{2}} : \frac{2 ( 3 - tan ( x ) + x sec ^{2} ( x ) )}{( 3 - tan ( x ) ) ^{2}}

= \frac{2 ( 3 - tan ( x ) + x sec ^{2} ( x ) )}{( 3 - tan ( x ) ) ^{2}}

\frac{\partial}{\partial x} (sin (8 x - 9 y))

\frac{x}{2} + 3

\frac{\partial}{\partial x} (ln (x + 2 y + 6 z))

\frac{d}{d x} (A e^{- \frac{3}{2} x} + B e^{3 x} + C x e^{3 x} + d x^{2} e^{3 x})

\frac{d}{d x} ((x^{2} + 4 x - 5)^{4})

What is the derivative of f(x)=(2x)/(3-tan(x)) ?
The derivative of f(x)=(2x)/(3-tan(x)) is (2(3-tan(x)+xsec^2(x)))/((3-tan(x))^2)
What is the first derivative of f(x)=(2x)/(3-tan(x)) ?
The first derivative of f(x)=(2x)/(3-tan(x)) is (2(3-tan(x)+xsec^2(x)))/((3-tan(x))^2)