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Popular >

derivative of arctan(e^{3x})

Solution

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

Solution

\frac{3 e ^{3 x}}{e ^{6 x} + 1}

Solution steps

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

Apply the chain rule:

\frac{1}{( e ^{3 x} ) ^{2} + 1} \frac{d}{d x} (e^{3 x})

= \frac{1}{( e ^{3 x} ) ^{2} + 1} \frac{d}{d x} (e^{3 x})

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

= \frac{1}{( e ^{3 x} ) ^{2} + 1} e^{3 x} \cdot 3

Simplify

\frac{1}{( e ^{3 x} ) ^{2} + 1} e^{3 x} \cdot 3 : \frac{3 e ^{3 x}}{e ^{6 x} + 1}

= \frac{3 e ^{3 x}}{e ^{6 x} + 1}

Popular Examples

limit as x approaches 5 of 2/(x-5)

x \to 5 lim (\frac{2}{x - 5})

derivative of tan(sin(x))

\frac{d}{d x} (tan (sin (x)))

integral of 1/(x^2sqrt(3x^2+4))

\int \frac{1}{x ^{2} 3 x ^{2} + 4} d x

derivative of y=1n(x^3)derivative of

y = 1 n (x^{3})

(\partial)/(\partial y)(x/(x^2+y^2+z^2))

\frac{\partial}{\partial y} (\frac{x}{x ^{2} + y ^{2} + z ^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of arctan(e^{3x}) ?
The derivative of arctan(e^{3x}) is (3e^{3x})/(e^{6x)+1}
What is the first derivative of arctan(e^{3x}) ?
The first derivative of arctan(e^{3x}) is (3e^{3x})/(e^{6x)+1}