What is the derivative of tan(sqrt(3x)) ?

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

What is the first derivative of tan(sqrt(3x)) ?

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

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\frac{d}{d x} (tan (3 x))

\frac{3 sec ^{2} ( 3 x )}{2 x}

Solution steps

\frac{d}{d x} (tan (3 x))

Simplify

tan (3 x) : tan (3 x)

= \frac{d}{d x} (tan (3 x))

Apply the chain rule:

sec^{2} (3 x) \frac{d}{d x} (3 x)

= sec^{2} (3 x) \frac{d}{d x} (3 x)

\frac{d}{d x} (3 x) = \frac{3}{2 x}

= sec^{2} (3 x) \frac{3}{2 x}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 sec ^{2} ( 3 x )}{2 x}

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