What is the derivative of ((3x+1)/(tan(x))) ?

The derivative of ((3x+1)/(tan(x))) is (3tan(x)-sec^2(x)(3x+1))/(tan^2(x))

What is the first derivative of ((3x+1)/(tan(x))) ?

The first derivative of ((3x+1)/(tan(x))) is (3tan(x)-sec^2(x)(3x+1))/(tan^2(x))

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\frac{d}{d x} (\frac{( 3 x + 1 )}{tan ( x )})

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

Solution steps

\frac{d}{d x} (\frac{( 3 x + 1 )}{tan ( x )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x + 1 ) tan ( x ) - \frac{d}{d x} ( tan ( x ) ) ( 3 x + 1 )}{( tan ( x ) ) ^{2}}

\frac{d}{d x} (3 x + 1) = 3

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

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

Simplify

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

2 x

f (x) = \frac{x}{7 - x}

h \to 0 lim (5 h^{2} + 8 h - 12)

\int_{- 5}^{2} (x^{2} + 3 x - 10) d x

\frac{1}{s ^{2} + 4 s + 5}

What is the derivative of ((3x+1)/(tan(x))) ?
The derivative of ((3x+1)/(tan(x))) is (3tan(x)-sec^2(x)(3x+1))/(tan^2(x))
What is the first derivative of ((3x+1)/(tan(x))) ?
The first derivative of ((3x+1)/(tan(x))) is (3tan(x)-sec^2(x)(3x+1))/(tan^2(x))