What is the derivative of sec(x+tan(x)) ?

The derivative of sec(x+tan(x)) is -1/(-1+sin(x))

What is the first derivative of sec(x+tan(x)) ?

The first derivative of sec(x+tan(x)) is -1/(-1+sin(x))

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

- \frac{1}{- 1 + sin ( x )}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

sec (x) tan (x) + sec^{2} (x) : - \frac{1}{- 1 + sin ( x )}

= - \frac{1}{- 1 + sin ( x )}

\frac{13}{x}

f (x) = 2 x^{4} - 6 x^{2}, at x = 1

x y 2 = 2 + x y

\int_{0}^{1} 2 x^{2} d x

\int \frac{1}{x ^{2} - 2 x - 8} d x

What is the derivative of sec(x+tan(x)) ?
The derivative of sec(x+tan(x)) is -1/(-1+sin(x))
What is the first derivative of sec(x+tan(x)) ?
The first derivative of sec(x+tan(x)) is -1/(-1+sin(x))