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)}

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

- \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}}

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)}