What is the derivative of f(x)=(7+tan(x))/(5-tan(x)) ?

The derivative of f(x)=(7+tan(x))/(5-tan(x)) is (12sec^2(x))/((5-tan(x))^2)

What is the first derivative of f(x)=(7+tan(x))/(5-tan(x)) ?

The first derivative of f(x)=(7+tan(x))/(5-tan(x)) is (12sec^2(x))/((5-tan(x))^2)

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derivative of

f (x) = \frac{7 + tan ( x )}{5 - tan ( x )}

\frac{12 sec ^{2} ( x )}{( 5 - tan ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{7 + tan ( x )}{5 - tan ( x )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 7 + tan ( x ) ) ( 5 - tan ( x ) ) - \frac{d}{d x} ( 5 - tan ( x ) ) ( 7 + tan ( x ) )}{( 5 - tan ( x ) ) ^{2}}

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

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

= \frac{sec ^{2} ( x ) ( 5 - tan ( x ) ) - ( - sec ^{2} ( x ) ) ( 7 + tan ( x ) )}{( 5 - tan ( x ) ) ^{2}}

Simplify

\frac{sec ^{2} ( x ) ( 5 - tan ( x ) ) - ( - sec ^{2} ( x ) ) ( 7 + tan ( x ) )}{( 5 - tan ( x ) ) ^{2}} : \frac{12 sec ^{2} ( x )}{( 5 - tan ( x ) ) ^{2}}

= \frac{12 sec ^{2} ( x )}{( 5 - tan ( x ) ) ^{2}}

\frac{\partial}{\partial x} (- 3 y cos (3 x))

(x y^{2} - 3 y) d x + (x^{2} y - 3 x) d y = 0

\int \frac{1 - x}{3 e ^{x}} d x

x \to 3 lim (x^{2} - 4)

x \to 0 lim (\frac{( 1 + x ) ^{3} - 1}{x})

What is the derivative of f(x)=(7+tan(x))/(5-tan(x)) ?
The derivative of f(x)=(7+tan(x))/(5-tan(x)) is (12sec^2(x))/((5-tan(x))^2)
What is the first derivative of f(x)=(7+tan(x))/(5-tan(x)) ?
The first derivative of f(x)=(7+tan(x))/(5-tan(x)) is (12sec^2(x))/((5-tan(x))^2)