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

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

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

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

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derivative of

y = \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}}

\int sin^{3} (2 x) cos^{5} (2 x) d x

\int_{0}^{1} x^{2} 3 x^{2} d x

\frac{d}{d x} (ln (7 x^{2} + 3 y^{2}))

\frac{d}{d x} (\frac{x + 1}{x ^{5}})

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

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