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Popular >

derivative of (cos(x)/(e^{2x)}-2)

Solution

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

Solution

- \frac{sin ( x ) + 2 cos ( x )}{e ^{2 x}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (\frac{cos ( x )}{e ^{2 x}}) = - \frac{sin ( x ) + 2 cos ( x )}{e ^{2 x}}

\frac{d}{d x} (2) = 0

= - \frac{sin ( x ) + 2 cos ( x )}{e ^{2 x}} - 0

Simplify

= - \frac{sin ( x ) + 2 cos ( x )}{e ^{2 x}}

Popular Examples

y^{^{'}} + \frac{1}{x} y = 2

limit as n approaches infinity of (4/5)^n

n \to \infty lim ((\frac{4}{5})^{n})

integral from 0 to 6r of sqrt(36r^2-y^2)

\int_{0}^{6 r} 36 r^{2} - y^{2} d y

limit as x approaches infinity of ln(6x)

x \to \infty lim (ln (6 x))

y^3-(2x+6)+3xy^2y^'=0

y^{3} - (2 x + 6) + 3 x y^{2} y^{^{'}} = 0

Frequently Asked Questions (FAQ)

What is the derivative of (cos(x)/(e^{2x)}-2) ?
The derivative of (cos(x)/(e^{2x)}-2) is -(sin(x)+2cos(x))/(e^{2x)}
What is the first derivative of (cos(x)/(e^{2x)}-2) ?
The first derivative of (cos(x)/(e^{2x)}-2) is -(sin(x)+2cos(x))/(e^{2x)}