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Popular >

derivative of sqrt(2+6e^{ax)}

Solution

derivative of

2 + 6 e^{a x}

Solution

\frac{3 a e ^{a x}}{2 + 6 e ^{a x}}

Solution steps

\frac{d}{d x} (2 + 6 e^{a x})

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral from 1 to 2 of (-9x^2+4x)

\int_{1}^{2} (- 9 x^{2} + 4 x) d x

limit as x approaches 0 of 4/(x+4h)

x \to 0 lim (\frac{4}{x + 4 h})

tangent of f(x)=4x^2+3x,(-3,27)tangent of

f (x) = 4 x^{2} + 3 x, (- 3, 27)

limit as x approaches infinity of 2x-x^2

x \to \infty lim (2 x - x^{2})

(\partial)/(\partial x)(e^{2xyz-3})

\frac{\partial}{\partial x} (e^{2 x yz - 3})

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(2+6e^{ax)} ?
The derivative of sqrt(2+6e^{ax)} is (3ae^{ax})/(sqrt(2+6e^{ax))}
What is the first derivative of sqrt(2+6e^{ax)} ?
The first derivative of sqrt(2+6e^{ax)} is (3ae^{ax})/(sqrt(2+6e^{ax))}