derivative of ln(sin(x^2))

解答

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

2 x cot (x^{2})

求解步骤

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

使用连锁律:

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

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

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

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

化简

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

= 2 x cot (x^{2})

\frac{d}{d x} (\frac{1}{f ( x ) ^{2} ( x )})

s l o p e - 10 x^{3} + 6 x^{40} y + y^{4} = 3

\int \frac{x ^{3}}{1 - x ^{2}} d x

x \to 4 - lim (2 - x - x^{2})

d er i v a t i v e f (x) = (x^{3} + 9) e^{x}