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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

f (x) = \frac{4 x}{x + 3}, (1, 1)

\frac{d}{d θ} (cos (θ) - θ sin (θ))

9 x^{2}, 8 x^{4} - 8 x^{2}

\frac{d y}{d x} + 2 x^{2} = 0

\int \frac{e ^{x}}{e ^{x} + 6} d x

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