What is the derivative of sec(xdx) ?

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

What is the first derivative of sec(xdx) ?

The first derivative of sec(xdx) 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))

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