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

The derivative of (sin(2x)/(cos(2x))) is sec^2(2x)*2

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

The first derivative of (sin(2x)/(cos(2x))) is sec^2(2x)*2

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\frac{d}{d x} (\frac{sin ( 2 x )}{cos ( 2 x )})

sec^{2} (2 x) \cdot 2

Solution steps

\frac{d}{d x} (\frac{sin ( 2 x )}{cos ( 2 x )})

Simplify

\frac{sin ( 2 x )}{cos ( 2 x )} : tan (2 x)

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

Apply the chain rule:

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

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

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

= sec^{2} (2 x) \cdot 2

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