What is the derivative of (e^{x^2}/(cos(3x))) ?

The derivative of (e^{x^2}/(cos(3x))) is e^{x^2}*2xsec(3x)+sec(3x)tan(3x)*3e^{x^2}

What is the first derivative of (e^{x^2}/(cos(3x))) ?

The first derivative of (e^{x^2}/(cos(3x))) is e^{x^2}*2xsec(3x)+sec(3x)tan(3x)*3e^{x^2}

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\frac{d}{d x} (\frac{e ^{x^{2}}}{cos ( 3 x )})

e^{x^{2}} \cdot 2 x sec (3 x) + sec (3 x) tan (3 x) \cdot 3 e^{x^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x^{2}}}{cos ( 3 x )})

Simplify

\frac{e ^{x^{2}}}{cos ( 3 x )} : e^{x^{2}} sec (3 x)

= \frac{d}{d x} (e^{x^{2}} sec (3 x))

Apply the Product Rule:

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

f = e^{x^{2}}, g = sec (3 x)

= \frac{d}{d x} (e^{x^{2}}) sec (3 x) + \frac{d}{d x} (sec (3 x)) e^{x^{2}}

\frac{d}{d x} (e^{x^{2}}) = e^{x^{2}} \cdot 2 x

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

= e^{x^{2}} \cdot 2 x sec (3 x) + sec (3 x) tan (3 x) \cdot 3 e^{x^{2}}

\frac{d}{d x} (e^{2 x} sin (7 x))

\frac{d y}{d t} + e^{t} y = - 7 e^{t}

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5 ln (x^{2}), x = 1

\int (\frac{9}{x}) d x

What is the derivative of (e^{x^2}/(cos(3x))) ?
The derivative of (e^{x^2}/(cos(3x))) is e^{x^2}*2xsec(3x)+sec(3x)tan(3x)*3e^{x^2}
What is the first derivative of (e^{x^2}/(cos(3x))) ?
The first derivative of (e^{x^2}/(cos(3x))) is e^{x^2}*2xsec(3x)+sec(3x)tan(3x)*3e^{x^2}