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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derivative of

\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{d}{d θ} (sin (θ) + 2 cos (θ))

\int \frac{24 x ^{6} - 24 x ^{4} + x}{x} d x

\int_{- y}^{y} ∣ x ∣ d x

x d y = d x

\frac{\partial}{\partial x} (\frac{6 x}{9 + x ^{2} + y ^{2}})

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)