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Popular >

derivative of arcsin(e^{3x})

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of 6xcos(3x^2)

\int 6 x cos (3 x^{2}) d x

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

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

limit as x approaches pi of x

x \to π lim (x)

inverse oflaplace 1/(s^2+2*pi*s+pi^2)inverse laplace

\frac{1}{s ^{2} + 2 \cdot π \cdot s + π ^{2}}

sum from n=3 to infinity of e^{5-6n}

n = 3 \sum \infty e^{5 - 6 n}

Frequently Asked Questions (FAQ)

What is the derivative of arcsin(e^{3x}) ?
The derivative of arcsin(e^{3x}) is (3e^{3x})/(sqrt(1-e^{6x))}
What is the first derivative of arcsin(e^{3x}) ?
The first derivative of arcsin(e^{3x}) is (3e^{3x})/(sqrt(1-e^{6x))}