What is the derivative of (e^x/(cos(3x))) ?

The derivative of (e^x/(cos(3x))) is e^xsec(3x)+sec(3x)tan(3x)*3e^x

What is the first derivative of (e^x/(cos(3x))) ?

The first derivative of (e^x/(cos(3x))) is e^xsec(3x)+sec(3x)tan(3x)*3e^x

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\frac{d}{d x} (\frac{e ^{x}}{cos ( 3 x )})

e^{x} sec (3 x) + sec (3 x) tan (3 x) \cdot 3 e^{x}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{cos ( 3 x )})

Simplify

\frac{e ^{x}}{cos ( 3 x )} : e^{x} sec (3 x)

= \frac{d}{d x} (e^{x} sec (3 x))

Apply the Product Rule:

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

f = e^{x}, g = sec (3 x)

= \frac{d}{d x} (e^{x}) sec (3 x) + \frac{d}{d x} (sec (3 x)) e^{x}

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

\frac{d}{d x} (sec (3 x)) = sec (3 x) tan (3 x) \cdot 3

= e^{x} sec (3 x) + sec (3 x) tan (3 x) \cdot 3 e^{x}

\int cot^{2} (x) csc^{2} (x) d x

\int 7 x^{3} e^{x^{4}} d x

\frac{d}{d x} ((4 x^{2} - 5)^{3})

x y^{^{'}} - 2 y - 8 = 0

f (x) = 3 x (18 x^{4} + \frac{13}{x + 1})

What is the derivative of (e^x/(cos(3x))) ?
The derivative of (e^x/(cos(3x))) is e^xsec(3x)+sec(3x)tan(3x)*3e^x
What is the first derivative of (e^x/(cos(3x))) ?
The first derivative of (e^x/(cos(3x))) is e^xsec(3x)+sec(3x)tan(3x)*3e^x