What is the derivative of sqrt(1+2e^{3x)} ?

The derivative of sqrt(1+2e^{3x)} is (3e^{3x})/(sqrt(1+2e^{3x))}

What is the first derivative of sqrt(1+2e^{3x)} ?

The first derivative of sqrt(1+2e^{3x)} is (3e^{3x})/(sqrt(1+2e^{3x))}

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

\frac{3 e ^{3 x}}{1 + 2 e ^{3 x}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (1 + 2 e^{3 x}) = 6 e^{3 x}

= \frac{1}{2 1 + 2 e ^{3 x}} \cdot 6 e^{3 x}

Simplify

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

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

What is the derivative of sqrt(1+2e^{3x)} ?
The derivative of sqrt(1+2e^{3x)} is (3e^{3x})/(sqrt(1+2e^{3x))}
What is the first derivative of sqrt(1+2e^{3x)} ?
The first derivative of sqrt(1+2e^{3x)} is (3e^{3x})/(sqrt(1+2e^{3x))}