What is the derivative of 8sec(xtan(x)) ?

The derivative of 8sec(xtan(x)) is 8(-sec(x)+2sec^3(x))

What is the first derivative of 8sec(xtan(x)) ?

The first derivative of 8sec(xtan(x)) is 8(-sec(x)+2sec^3(x))

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\frac{d}{d x} (8 sec (x) tan (x))

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

Solution steps

\frac{d}{d x} (8 sec (x) tan (x))

Take the constant out:

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

= 8 \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)

= 8 (\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)

= 8 (sec (x) tan (x) tan (x) + sec^{2} (x) sec (x))

Simplify

8 (sec (x) tan (x) tan (x) + sec^{2} (x) sec (x)) : 8 (- sec (x) + 2 sec^{3} (x))

= 8 (- sec (x) + 2 sec^{3} (x))

\frac{\partial}{\partial z} (22 cos (x) y z^{2})

\int - \frac{1}{16} sin (4 x) d x

x \to 64 lim (x^{\frac{4}{3}})

y = x^{2} + 5 x, (- 4, - 4)

\frac{d}{d x} (x - \frac{x ^{2}}{800})

What is the derivative of 8sec(xtan(x)) ?
The derivative of 8sec(xtan(x)) is 8(-sec(x)+2sec^3(x))
What is the first derivative of 8sec(xtan(x)) ?
The first derivative of 8sec(xtan(x)) is 8(-sec(x)+2sec^3(x))