What is the derivative of-2sec^2(xtan(x)) ?

The derivative of-2sec^2(xtan(x)) is -2(-2sec^2(x)+3sec^4(x))

What is the first derivative of-2sec^2(xtan(x)) ?

The first derivative of-2sec^2(xtan(x)) is -2(-2sec^2(x)+3sec^4(x))

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

- 2 (- 2 sec^{2} (x) + 3 sec^{4} (x))

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = sec^{2} (x), g = tan (x)

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

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

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

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

Simplify

- 2 (2 sec^{2} (x) tan (x) tan (x) + sec^{2} (x) sec^{2} (x)) : - 2 (- 2 sec^{2} (x) + 3 sec^{4} (x))

= - 2 (- 2 sec^{2} (x) + 3 sec^{4} (x))

x \to 0 lim (- csc^{2} (x))

\frac{d}{d x} (3 a^{3 x})

y = sin^{5} (3 x)

\int 2 x + 3 d x

\frac{d}{d x} (5 - 6 x)

What is the derivative of-2sec^2(xtan(x)) ?
The derivative of-2sec^2(xtan(x)) is -2(-2sec^2(x)+3sec^4(x))
What is the first derivative of-2sec^2(xtan(x)) ?
The first derivative of-2sec^2(xtan(x)) is -2(-2sec^2(x)+3sec^4(x))