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Popular Calculus >

derivative of-3/(x^2+4e^{2x})

Solution

\frac{d}{d x} (- \frac{3}{x ^{2}} + 4 e^{2 x})

Solution

\frac{6}{x ^{3}} + 8 e^{2 x}

Solution steps

\frac{d}{d x} (- \frac{3}{x ^{2}} + 4 e^{2 x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d}{d x} (\frac{3}{x ^{2}}) + \frac{d}{d x} (4 e^{2 x})

\frac{d}{d x} (\frac{3}{x ^{2}}) = - \frac{6}{x ^{3}}

\frac{d}{d x} (4 e^{2 x}) = 8 e^{2 x}

= - (- \frac{6}{x ^{3}}) + 8 e^{2 x}

Simplify

= \frac{6}{x ^{3}} + 8 e^{2 x}

Graph

Popular Examples

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\frac{\partial}{\partial y} (2 x + 3 y - 7)

integral of 1 (cos(2x))

\int \frac{d}{1} (cos (2 x)) d x

sum from n=1 to infinity of (1-p)^{3n}

n = 1 \sum \infty (1 - p)^{3 n}

limit as x approaches 1 of 3x^2-1

x \to 1 lim (3 x^{2} - 1)

Frequently Asked Questions (FAQ)

What is the derivative of-3/(x^2+4e^{2x}) ?
The derivative of-3/(x^2+4e^{2x}) is 6/(x^3)+8e^{2x}
What is the first derivative of-3/(x^2+4e^{2x}) ?
The first derivative of-3/(x^2+4e^{2x}) is 6/(x^3)+8e^{2x}