What is the derivative of (csc(xtan(x))/(cos(x))) ?

The derivative of (csc(xtan(x))/(cos(x))) is 2sec^2(x)tan(x)

What is the first derivative of (csc(xtan(x))/(cos(x))) ?

The first derivative of (csc(xtan(x))/(cos(x))) is 2sec^2(x)tan(x)

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\frac{d}{d x} (\frac{csc ( x ) tan ( x )}{cos ( x )})

2 sec^{2} (x) tan (x)

Solution steps

\frac{d}{d x} (\frac{csc ( x ) tan ( x )}{cos ( x )})

Simplify

\frac{csc ( x ) tan ( x )}{cos ( x )} : sec^{2} (x)

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

Apply the chain rule:

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

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

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

= 2 sec (x) sec (x) tan (x)

Simplify

2 sec (x) sec (x) tan (x) : 2 sec^{2} (x) tan (x)

= 2 sec^{2} (x) tan (x)

What is the derivative of (csc(xtan(x))/(cos(x))) ?
The derivative of (csc(xtan(x))/(cos(x))) is 2sec^2(x)tan(x)
What is the first derivative of (csc(xtan(x))/(cos(x))) ?
The first derivative of (csc(xtan(x))/(cos(x))) is 2sec^2(x)tan(x)