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Popular >

derivative of y=sqrt(1+2e^{8x)}

Solution

derivative of

y = 1 + 2 e^{8 x}

Solution

\frac{8 e ^{8 x}}{1 + 2 e ^{8 x}}

Solution steps

\frac{d}{d x} (1 + 2 e^{8 x})

Apply the chain rule:

\frac{1}{2 1 + 2 e ^{8 x}} \frac{d}{d x} (1 + 2 e^{8 x})

= \frac{1}{2 1 + 2 e ^{8 x}} \frac{d}{d x} (1 + 2 e^{8 x})

\frac{d}{d x} (1 + 2 e^{8 x}) = 16 e^{8 x}

= \frac{1}{2 1 + 2 e ^{8 x}} \cdot 16 e^{8 x}

Simplify

\frac{1}{2 1 + 2 e ^{8 x}} \cdot 16 e^{8 x} : \frac{8 e ^{8 x}}{1 + 2 e ^{8 x}}

= \frac{8 e ^{8 x}}{1 + 2 e ^{8 x}}

Popular Examples

sum from n=1 to infinity of 1/(7n^2+n+6)

n = 1 \sum \infty \frac{1}{7 n ^{2} + n + 6}

derivative of-ce^{-x}

\frac{d}{d x} (- c e^{- x})

integral of 1/((2x-3)(3x^2+x))

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

integral of 2x^5e^x

\int 2 x^{5} e^{x} d x

integral from 0 to 1 of xe^x-e^x

\int_{0}^{1} x e^{x} - e^{x} d x

Frequently Asked Questions (FAQ)

What is the derivative of y=sqrt(1+2e^{8x)} ?
The derivative of y=sqrt(1+2e^{8x)} is (8e^{8x})/(sqrt(1+2e^{8x))}
What is the first derivative of y=sqrt(1+2e^{8x)} ?
The first derivative of y=sqrt(1+2e^{8x)} is (8e^{8x})/(sqrt(1+2e^{8x))}