What is the derivative of sqrt(tan^2(3x+1)) ?

The derivative of sqrt(tan^2(3x+1)) is 3sec(3x)tan(3x)

What is the first derivative of sqrt(tan^2(3x+1)) ?

The first derivative of sqrt(tan^2(3x+1)) is 3sec(3x)tan(3x)

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\frac{d}{d x} (tan^{2} (3 x) + 1)

3 sec (3 x) tan (3 x)

Solution steps

\frac{d}{d x} (tan^{2} (3 x) + 1)

Apply the chain rule:

\frac{1}{2 tan ^{2} ( 3 x ) + 1} \frac{d}{d x} (tan^{2} (3 x) + 1)

= \frac{1}{2 tan ^{2} ( 3 x ) + 1} \frac{d}{d x} (tan^{2} (3 x) + 1)

\frac{d}{d x} (tan^{2} (3 x) + 1) = 6 sec^{2} (3 x) tan (3 x)

= \frac{1}{2 tan ^{2} ( 3 x ) + 1} \cdot 6 sec^{2} (3 x) tan (3 x)

Simplify

\frac{1}{2 tan ^{2} ( 3 x ) + 1} \cdot 6 sec^{2} (3 x) tan (3 x) : 3 sec (3 x) tan (3 x)

= 3 sec (3 x) tan (3 x)

What is the derivative of sqrt(tan^2(3x+1)) ?
The derivative of sqrt(tan^2(3x+1)) is 3sec(3x)tan(3x)
What is the first derivative of sqrt(tan^2(3x+1)) ?
The first derivative of sqrt(tan^2(3x+1)) is 3sec(3x)tan(3x)