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))

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derivative of

\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))

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))