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

The derivative of sin(sqrt(ln(tan(x)))) is (csc(2x)cos(sqrt(ln(tan(x)))))/(sqrt(ln(tan(x))))

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

The first derivative of sin(sqrt(ln(tan(x)))) is (csc(2x)cos(sqrt(ln(tan(x)))))/(sqrt(ln(tan(x))))

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

\frac{csc ( 2 x ) cos ( ln ( tan ( x ) ) )}{ln ( tan ( x ) )}

Solution steps

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

Apply the chain rule:

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

= cos (ln (tan (x))) \frac{d}{d x} (ln (tan (x)))

\frac{d}{d x} (ln (tan (x))) = \frac{csc ( 2 x )}{ln ( tan ( x ) )}

= cos (ln (tan (x))) \frac{csc ( 2 x )}{ln ( tan ( x ) )}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{csc ( 2 x ) cos ( ln ( tan ( x ) ) )}{ln ( tan ( x ) )}

\int 6 t d t

y = (x + \frac{1}{x}) (x - \frac{1}{x})

\frac{d}{d x} (\frac{cos ( x ^{3} )}{e ^{x}})

f (x) = x^{2} - 4

x^{3} - x

What is the derivative of sin(sqrt(ln(tan(x)))) ?
The derivative of sin(sqrt(ln(tan(x)))) is (csc(2x)cos(sqrt(ln(tan(x)))))/(sqrt(ln(tan(x))))
What is the first derivative of sin(sqrt(ln(tan(x)))) ?
The first derivative of sin(sqrt(ln(tan(x)))) is (csc(2x)cos(sqrt(ln(tan(x)))))/(sqrt(ln(tan(x))))