What is the derivative of ln(sin(7x^2-pi)) ?

The derivative of ln(sin(7x^2-pi)) is 14xcot(7x^2)

What is the first derivative of ln(sin(7x^2-pi)) ?

The first derivative of ln(sin(7x^2-pi)) is 14xcot(7x^2)

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\frac{d}{d x} (ln (sin (7 x^{2} - π)))

14 x cot (7 x^{2})

Solution steps

\frac{d}{d x} (ln (sin (7 x^{2} - π)))

Simplify

ln (sin (7 x^{2} - π)) : ln (- sin (7 x^{2}))

= \frac{d}{d x} (ln (- sin (7 x^{2})))

Apply the chain rule:

\frac{1}{- sin ( 7 x ^{2} )} \frac{d}{d x} (- sin (7 x^{2}))

= \frac{1}{- sin ( 7 x ^{2} )} \frac{d}{d x} (- sin (7 x^{2}))

\frac{d}{d x} (- sin (7 x^{2})) = - cos (7 x^{2}) \cdot 14 x

= \frac{1}{- sin ( 7 x ^{2} )} (- cos (7 x^{2}) \cdot 14 x)

Simplify

\frac{1}{- sin ( 7 x ^{2} )} (- cos (7 x^{2}) \cdot 14 x) : 14 x cot (7 x^{2})

= 14 x cot (7 x^{2})

\frac{d}{d x} (x - x^{\frac{2}{3}})

\frac{d}{d x} (- 2 cos (x))

y^{^{'}} = \frac{y}{1 - x} + \frac{2}{1 - x} + 3

\frac{d}{d x} (1 + tan (x))

f (X) = 4 X^{3} - 1

What is the derivative of ln(sin(7x^2-pi)) ?
The derivative of ln(sin(7x^2-pi)) is 14xcot(7x^2)
What is the first derivative of ln(sin(7x^2-pi)) ?
The first derivative of ln(sin(7x^2-pi)) is 14xcot(7x^2)