What is the derivative of 5sec(xtan(x)) ?

The derivative of 5sec(xtan(x)) is 5(-sec(x)+2sec^3(x))

What is the first derivative of 5sec(xtan(x)) ?

The first derivative of 5sec(xtan(x)) is 5(-sec(x)+2sec^3(x))

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\frac{d}{d x} (5 sec (x) tan (x))

5 (- sec (x) + 2 sec^{3} (x))

Solution steps

\frac{d}{d x} (5 sec (x) tan (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (sec (x) tan (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sec (x), g = tan (x)

= 5 (\frac{d}{d x} (sec (x)) tan (x) + \frac{d}{d x} (tan (x)) sec (x))

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

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

= 5 (sec (x) tan (x) tan (x) + sec^{2} (x) sec (x))

Simplify

5 (sec (x) tan (x) tan (x) + sec^{2} (x) sec (x)) : 5 (- sec (x) + 2 sec^{3} (x))

= 5 (- sec (x) + 2 sec^{3} (x))

What is the derivative of 5sec(xtan(x)) ?
The derivative of 5sec(xtan(x)) is 5(-sec(x)+2sec^3(x))
What is the first derivative of 5sec(xtan(x)) ?
The first derivative of 5sec(xtan(x)) is 5(-sec(x)+2sec^3(x))