What is the derivative of ln((tan(sqrt(x))^3)) ?

The derivative of ln((tan(sqrt(x))^3)) is (3sec^2(sqrt(x)))/(2sqrt(x)tan(\sqrt{x))}

What is the first derivative of ln((tan(sqrt(x))^3)) ?

The first derivative of ln((tan(sqrt(x))^3)) is (3sec^2(sqrt(x)))/(2sqrt(x)tan(\sqrt{x))}

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

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

Solution steps

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

Apply the chain rule:

\frac{1}{( tan ( x ) ) ^{3}} \frac{d}{d x} ((tan (x))^{3})

= \frac{1}{( tan ( x ) ) ^{3}} \frac{d}{d x} ((tan (x))^{3})

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

= \frac{1}{( tan ( x ) ) ^{3}} \cdot \frac{3 sec ^{2} ( x ) tan ^{2} ( x )}{2 x}

Simplify

\frac{1}{tan ^{3} ( x )} \cdot \frac{3 sec ^{2} ( x ) tan ^{2} ( x )}{2 x} : \frac{3 sec ^{2} ( x )}{2 x tan ( x )}

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

What is the derivative of ln((tan(sqrt(x))^3)) ?
The derivative of ln((tan(sqrt(x))^3)) is (3sec^2(sqrt(x)))/(2sqrt(x)tan(\sqrt{x))}
What is the first derivative of ln((tan(sqrt(x))^3)) ?
The first derivative of ln((tan(sqrt(x))^3)) is (3sec^2(sqrt(x)))/(2sqrt(x)tan(\sqrt{x))}