derivative of log_{5}(sin^2(x))

解答

\frac{d}{d x} (lo g_{5} (sin^{2} (x)))

\frac{sin ( 2 x )}{ln ( 5 ) sin ^{2} ( x )}

求解步骤

\frac{d}{d x} (lo g_{5} (sin^{2} (x)))

使用对数计算法则:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( sin ^{2} ( x ) )}{ln ( 5 )})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{ln ( 5 )} \frac{d}{d x} (ln (sin^{2} (x)))

使用连锁律:

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

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

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

= \frac{1}{ln ( 5 )} \cdot \frac{1}{sin ^{2} ( x )} sin (2 x)

化简

\frac{1}{ln ( 5 )} \cdot \frac{1}{sin ^{2} ( x )} sin (2 x) : \frac{sin ( 2 x )}{ln ( 5 ) sin ^{2} ( x )}

= \frac{sin ( 2 x )}{ln ( 5 ) sin ^{2} ( x )}

\int 441 - x^{2} d x

x \to 0 - lim (\frac{x + 1}{x ^{2}})

\int 17 sin^{3} (x co) s^{2} x d x

\frac{d y}{d x} = 1 0^{- 21} \cdot y^{3}

d er i v a t i v e y = e^{a r c t a n (3 t^{2})}