What is the derivative of 6sec(xtan(x)) ?

The derivative of 6sec(xtan(x)) is 6(-sec(x)+2sec^3(x))

What is the first derivative of 6sec(xtan(x)) ?

The first derivative of 6sec(xtan(x)) is 6(-sec(x)+2sec^3(x))

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\frac{d}{d x} (6 sec (x) tan (x))

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

Solution steps

\frac{d}{d x} (6 sec (x) tan (x))

Take the constant out:

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

= 6 \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)

= 6 (\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)

= 6 (sec (x) tan (x) tan (x) + sec^{2} (x) sec (x))

Simplify

6 (sec (x) tan (x) tan (x) + sec^{2} (x) sec (x)) : 6 (- sec (x) + 2 sec^{3} (x))

= 6 (- sec (x) + 2 sec^{3} (x))

\int_{0}^{\infty} e^{\frac{x}{3}} d x

x^{2} \frac{d y}{d x} + 4 x y - y^{3} = 0

\int_{0}^{1} 2 π (x) (8 - 7 x - x^{2}) d x

\int_{0}^{1} \frac{5}{x ^{5}} d x

\frac{d}{d x} (\frac{24}{x ^{2} + 12})

What is the derivative of 6sec(xtan(x)) ?
The derivative of 6sec(xtan(x)) is 6(-sec(x)+2sec^3(x))
What is the first derivative of 6sec(xtan(x)) ?
The first derivative of 6sec(xtan(x)) is 6(-sec(x)+2sec^3(x))