What is (\partial)/(\partial x)(tan(sqrt(3x))) ?

The answer to (\partial)/(\partial x)(tan(sqrt(3x))) is (sqrt(3)sec^2(sqrt(3)sqrt(x)))/(2sqrt(x))

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(\partial)/(\partial x)(tan(sqrt(3x)))

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

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

Solution steps

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

Simplify

tan (3 x) : tan (3 x)

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

Apply the chain rule:

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

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

\frac{\partial}{\partial 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}

y^{^{''}} - 9 y^{^{'}} + 20 y = 0

x \to 4 lim (\frac{x - 5}{x - 4})

\frac{\partial}{\partial y} (\frac{y ^{2}}{x})

\frac{d}{d x} (\frac{x ^{4}}{4} - \frac{9}{2} x^{2} + 1)

\int (x + y)^{2} d x

What is (\partial)/(\partial x)(tan(sqrt(3x))) ?
The answer to (\partial)/(\partial x)(tan(sqrt(3x))) is (sqrt(3)sec^2(sqrt(3)sqrt(x)))/(2sqrt(x))