What is the derivative of e^{xsec(x}) ?

The derivative of e^{xsec(x}) is e^{xsec(x)}(sec(x)+xsec(x)tan(x))

What is the first derivative of e^{xsec(x}) ?

The first derivative of e^{xsec(x}) is e^{xsec(x)}(sec(x)+xsec(x)tan(x))

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\frac{d}{d x} (e^{x s e c (x)})

e^{x s e c (x)} (sec (x) + x sec (x) tan (x))

Solution steps

\frac{d}{d x} (e^{x s e c (x)})

Apply the chain rule:

e^{x s e c (x)} \frac{d}{d x} (x sec (x))

= e^{x s e c (x)} \frac{d}{d x} (x sec (x))

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

= e^{x s e c (x)} (sec (x) + x sec (x) tan (x))

What is the derivative of e^{xsec(x}) ?
The derivative of e^{xsec(x}) is e^{xsec(x)}(sec(x)+xsec(x)tan(x))
What is the first derivative of e^{xsec(x}) ?
The first derivative of e^{xsec(x}) is e^{xsec(x)}(sec(x)+xsec(x)tan(x))