What is the derivative of (4e^x/(cos(x))) ?

The derivative of (4e^x/(cos(x))) is 4sec(x)(e^x+e^xtan(x))

What is the first derivative of (4e^x/(cos(x))) ?

The first derivative of (4e^x/(cos(x))) is 4sec(x)(e^x+e^xtan(x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{4 e ^{x}}{cos ( x )})

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

Solution steps

\frac{d}{d x} (\frac{4 e ^{x}}{cos ( x )})

Simplify

\frac{4 e ^{x}}{cos ( x )} : 4 e^{x} sec (x)

= \frac{d}{d x} (4 e^{x} sec (x))

Take the constant out:

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

= 4 \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)

= 4 (\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)

= 4 (e^{x} sec (x) + sec (x) tan (x) e^{x})

Simplify

4 (e^{x} sec (x) + sec (x) tan (x) e^{x}) : 4 sec (x) (e^{x} + e^{x} tan (x))

= 4 sec (x) (e^{x} + e^{x} tan (x))

\int_{1}^{4} (x) d x

\frac{d y}{d x} - \frac{y}{x} = 6 x e^{x}

y^{^{''}} + 4 y^{^{'}} + 4 y = t^{- 2} e^{- 2 t}

\frac{d}{d x} (tan (x^{2} - 1))

y^{^{''}} - y^{^{'}} - 20 y = 0

What is the derivative of (4e^x/(cos(x))) ?
The derivative of (4e^x/(cos(x))) is 4sec(x)(e^x+e^xtan(x))
What is the first derivative of (4e^x/(cos(x))) ?
The first derivative of (4e^x/(cos(x))) is 4sec(x)(e^x+e^xtan(x))