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Popular Calculus >

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

Solution

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

Solution

2 e^{2 x} + 2 sin (2 x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

= e^{2 x} \cdot 2 - (- sin (2 x) \cdot 2)

Simplify

= 2 e^{2 x} + 2 sin (2 x)

Graph

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Frequently Asked Questions (FAQ)

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