What is the derivative of (8x/(5-tan(x))) ?

The derivative of (8x/(5-tan(x))) is (8(5-tan(x)+xsec^2(x)))/((5-tan(x))^2)

What is the first derivative of (8x/(5-tan(x))) ?

The first derivative of (8x/(5-tan(x))) is (8(5-tan(x)+xsec^2(x)))/((5-tan(x))^2)

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\frac{d}{d x} (\frac{8 x}{5 - tan ( x )})

\frac{8 ( 5 - tan ( x ) + x sec ^{2} ( x ) )}{( 5 - tan ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{8 x}{5 - tan ( x )})

Take the constant out:

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

= 8 \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}}

= 8 \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)

= 8 \cdot \frac{1 \cdot ( 5 - tan ( x ) ) - ( - sec ^{2} ( x ) ) x}{( 5 - tan ( x ) ) ^{2}}

Simplify

8 \cdot \frac{1 \cdot ( 5 - tan ( x ) ) - ( - sec ^{2} ( x ) ) x}{( 5 - tan ( x ) ) ^{2}} : \frac{8 ( 5 - tan ( x ) + x sec ^{2} ( x ) )}{( 5 - tan ( x ) ) ^{2}}

= \frac{8 ( 5 - tan ( x ) + x sec ^{2} ( x ) )}{( 5 - tan ( x ) ) ^{2}}

y^{^{'}} - \frac{6}{x} y = x^{- 4} y^{5}, y (1) = 1

\int_{0}^{\infty} 4 e^{- 4 x} d x

\int \frac{x}{x - 2} d x

x \to - 2 lim (\frac{5 x ^{2} + 6 x - 8}{x + 2})

\frac{d}{d x} ((x^{2} - 9)^{2})

What is the derivative of (8x/(5-tan(x))) ?
The derivative of (8x/(5-tan(x))) is (8(5-tan(x)+xsec^2(x)))/((5-tan(x))^2)
What is the first derivative of (8x/(5-tan(x))) ?
The first derivative of (8x/(5-tan(x))) is (8(5-tan(x)+xsec^2(x)))/((5-tan(x))^2)