What is the derivative of (3x+2/(cos(x))) ?

The derivative of (3x+2/(cos(x))) is (3cos(x)+sin(x)(3x+2))/(cos^2(x))

What is the first derivative of (3x+2/(cos(x))) ?

The first derivative of (3x+2/(cos(x))) is (3cos(x)+sin(x)(3x+2))/(cos^2(x))

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\frac{d}{d x} (\frac{3 x + 2}{cos ( x )})

\frac{3 cos ( x ) + sin ( x ) ( 3 x + 2 )}{cos ^{2} ( x )}

Solution steps

\frac{d}{d x} (\frac{3 x + 2}{cos ( x )})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (3 x + 2) = 3

\frac{d}{d x} (cos (x)) = - sin (x)

= \frac{3 cos ( x ) - ( - sin ( x ) ) ( 3 x + 2 )}{( cos ( x ) ) ^{2}}

Simplify

= \frac{3 cos ( x ) + sin ( x ) ( 3 x + 2 )}{cos ^{2} ( x )}

What is the derivative of (3x+2/(cos(x))) ?
The derivative of (3x+2/(cos(x))) is (3cos(x)+sin(x)(3x+2))/(cos^2(x))
What is the first derivative of (3x+2/(cos(x))) ?
The first derivative of (3x+2/(cos(x))) is (3cos(x)+sin(x)(3x+2))/(cos^2(x))