derivative of tan^{ln(5x}(cos(x)))

解答

\frac{d}{d x} (tan^{l n (5 x)} (cos (x)))

(\frac{ln ( tan ( cos ( x ) ) )}{x} - sec^{2} (cos (x)) sin (x) cot (cos (x)) ln (5 x)) (5 x)^{l n (t a n (c o s (x)))}

求解步骤

\frac{d}{d x} (tan^{l n (5 x)} (cos (x)))

使用指数法则:

a^{b} = e^{b l n (a)}

tan^{l n (5 x)} (cos (x)) = e^{l n (5 x) l n (t a n (c o s (x)))}

= \frac{d}{d x} (e^{l n (5 x) l n (t a n (c o s (x)))})

使用连锁律:

e^{l n (5 x) l n (t a n (c o s (x)))} \frac{d}{d x} (ln (5 x) ln (tan (cos (x))))

= e^{l n (5 x) l n (t a n (c o s (x)))} \frac{d}{d x} (ln (5 x) ln (tan (cos (x))))

\frac{d}{d x} (ln (5 x) ln (tan (cos (x)))) = \frac{ln ( tan ( cos ( x ) ) )}{x} - sec^{2} (cos (x)) sin (x) cot (cos (x)) ln (5 x)

= e^{l n (5 x) l n (t a n (c o s (x)))} (\frac{ln ( tan ( cos ( x ) ) )}{x} - sec^{2} (cos (x)) sin (x) cot (cos (x)) ln (5 x))

e^{l n (5 x) l n (t a n (c o s (x)))} = (5 x)^{l n (t a n (c o s (x)))}

= (\frac{ln ( tan ( cos ( x ) ) )}{x} - sec^{2} (cos (x)) sin (x) cot (cos (x)) ln (5 x)) (5 x)^{l n (t a n (c o s (x)))}

a re a - x^{2} + 2 x, y = x^{3} + x^{2} - 6 x

a re a y = x^{3} - 2 x^{2}, y = 2 x^{2} - 3 x

in v erse l a pl a ce \frac{2}{( ( s + 2 ) ( s ^{2} - 4 ) )}

\int \frac{2}{- x ^{2} + 4 x} d x

\frac{d}{d θ} (4 + 4 sin (θ))