What is the derivative of e^{sqrt(tan(3x)}) ?

The derivative of e^{sqrt(tan(3x)}) is (3e^{sqrt(tan(3x))}sec^2(3x))/(2sqrt(tan(3x)))

What is the first derivative of e^{sqrt(tan(3x)}) ?

The first derivative of e^{sqrt(tan(3x)}) is (3e^{sqrt(tan(3x))}sec^2(3x))/(2sqrt(tan(3x)))

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\frac{d}{d x} (e^{t a n (3 x)})

\frac{3 e ^{t a n (3 x)} sec ^{2} ( 3 x )}{2 tan ( 3 x )}

Solution steps

\frac{d}{d x} (e^{t a n (3 x)})

Apply the chain rule:

e^{t a n (3 x)} \frac{d}{d x} (tan (3 x))

= e^{t a n (3 x)} \frac{d}{d x} (tan (3 x))

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

= e^{t a n (3 x)} \frac{3 sec ^{2} ( 3 x )}{2 tan ( 3 x )}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 e ^{t a n (3 x)} sec ^{2} ( 3 x )}{2 tan ( 3 x )}

(9, 2), (- 2, 6)

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

\frac{( x ^{2} )}{5 + x}

\frac{d y}{d x} + \frac{y}{x} = 2 x^{2} y^{2}

\frac{d y}{d x} + y = x y^{4}

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