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))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\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 )}

\frac{d}{d x} (4 sin (x) cos (x))

\int \frac{2}{5} x d x

2 + x^{2}

n = 0 \sum \infty 2 (- \frac{2}{3})^{n}

\frac{1}{3} x^{3} - 3 x^{2} - 16 x + 8

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))