What is the derivative of (sec(x)dx) ?

The derivative of (sec(x)dx) is d(xsec(x)tan(x)+sec(x))

What is the first derivative of (sec(x)dx) ?

The first derivative of (sec(x)dx) is d(xsec(x)tan(x)+sec(x))

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

d (x sec (x) tan (x) + sec (x))

Solution steps

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

Treat

d

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = sec (x), g = x

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

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

\frac{d x}{d x} = 1

= d (sec (x) tan (x) x + 1 \cdot sec (x))

Simplify

= d (x sec (x) tan (x) + sec (x))

\int \frac{1}{x ^{2} + 6 x + 15} d x

y = \frac{1}{2} x + \frac{1}{4} x sin (2 x)

f (x) = x x, at x = 4

\int \frac{( e ^{x} )}{e ^{x} ( e ^{x} - 3 )} d x

\int \frac{( x ^{3} )}{x ^{2} + 81} d x

What is the derivative of (sec(x)dx) ?
The derivative of (sec(x)dx) is d(xsec(x)tan(x)+sec(x))
What is the first derivative of (sec(x)dx) ?
The first derivative of (sec(x)dx) is d(xsec(x)tan(x)+sec(x))