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Popular >

derivative of xtan(2sqrt(x))

Solution

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

Solution

tan (2 x) + x sec^{2} (2 x)

Solution steps

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

Apply the Product Rule:

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

f = x, g = tan (2 x)

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

\frac{d x}{d x} = 1

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

= 1 \cdot tan (2 x) + \frac{sec ^{2} ( 2 x )}{x} x

Simplify

1 \cdot tan (2 x) + \frac{sec ^{2} ( 2 x )}{x} x : tan (2 x) + x sec^{2} (2 x)

= tan (2 x) + x sec^{2} (2 x)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of xtan(2sqrt(x)) ?
The derivative of xtan(2sqrt(x)) is tan(2sqrt(x))+sqrt(x)sec^2(2sqrt(x))
What is the first derivative of xtan(2sqrt(x)) ?
The first derivative of xtan(2sqrt(x)) is tan(2sqrt(x))+sqrt(x)sec^2(2sqrt(x))