What is the derivative of (e^x/(cos(x))) ?

The derivative of (e^x/(cos(x))) is (e^x+e^xtan(x))/(cos(x))

What is the first derivative of (e^x/(cos(x))) ?

The first derivative of (e^x/(cos(x))) is (e^x+e^xtan(x))/(cos(x))

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\frac{d}{d x} (\frac{e ^{x}}{cos ( x )})

\frac{e ^{x} + e ^{x} tan ( x )}{cos ( x )}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{cos ( x )})

Simplify

\frac{e ^{x}}{cos ( x )} : e^{x} sec (x)

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

Apply the Product Rule:

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

f = e^{x}, g = sec (x)

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

\frac{d}{d x} (e^{x}) = e^{x}

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

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

Rewrite using trig identities

= \frac{e ^{x} + e ^{x} tan ( x )}{cos ( x )}

What is the derivative of (e^x/(cos(x))) ?
The derivative of (e^x/(cos(x))) is (e^x+e^xtan(x))/(cos(x))
What is the first derivative of (e^x/(cos(x))) ?
The first derivative of (e^x/(cos(x))) is (e^x+e^xtan(x))/(cos(x))