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Popular >

derivative of e^{2x}tan(2x)

Solution

derivative of

e^{2 x} tan (2 x)

Solution

e^{2 x} \cdot 2 tan (2 x) + sec^{2} (2 x) \cdot 2 e^{2 x}

Solution steps

\frac{d}{d x} (e^{2 x} tan (2 x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{2 x}, g = tan (2 x)

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

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

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

= e^{2 x} \cdot 2 tan (2 x) + sec^{2} (2 x) \cdot 2 e^{2 x}

Popular Examples

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\int_{0}^{2} \frac{4 x + 3}{x ^{4}} d x

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Frequently Asked Questions (FAQ)

What is the derivative of e^{2x}tan(2x) ?
The derivative of e^{2x}tan(2x) is e^{2x}*2tan(2x)+sec^2(2x)*2e^{2x}
What is the first derivative of e^{2x}tan(2x) ?
The first derivative of e^{2x}tan(2x) is e^{2x}*2tan(2x)+sec^2(2x)*2e^{2x}