What is the derivative of (tan(3x)/(x^2)) ?

The derivative of (tan(3x)/(x^2)) is (3xsec^2(3x)-2tan(3x))/(x^3)

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

The first derivative of (tan(3x)/(x^2)) is (3xsec^2(3x)-2tan(3x))/(x^3)

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

\frac{sec ^{2} ( 3 x ) \cdot 3 x ^{2} - 2 x tan ( 3 x )}{( x ^{2} ) ^{2}} : \frac{3 x sec ^{2} ( 3 x ) - 2 tan ( 3 x )}{x ^{3}}

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

\frac{\partial}{\partial y} (5 y)

x \to \infty lim (x \frac{1}{x})

\int_{2}^{3} \frac{39}{3 - x} d x

\int (- 3 x) d x

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

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