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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d x}{d x} = 1

= \frac{sec ^{2} ( x ) x - 1 \cdot tan ( x )}{x ^{2}}

Simplify

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

n = 0 \sum \infty \frac{n}{3 ^{n}}

f (x) = arccos (2 x)

x \to 0 + lim (\frac{e ^{\frac{1}{x}}}{x})

(3 x + 4)^{2}

\frac{d}{d t} (2 t - 1)

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