derivative of e^{ktan(sqrt(3x)})

解答

\frac{d}{d x} (e^{k t a n (3 x)})

\frac{3 k e ^{k t a n (3 x)} sec ^{2} ( 3 x )}{2 x}

求解步骤

\frac{d}{d x} (e^{k t a n (3 x)})

化简

e^{k t a n (3 x)} : e^{k t a n (3 x)}

= \frac{d}{d x} (e^{k t a n (3 x)})

使用连锁律:

e^{k t a n (3 x)} \frac{d}{d x} (k tan (3 x))

= e^{k t a n (3 x)} \frac{d}{d x} (k tan (3 x))

\frac{d}{d x} (k tan (3 x)) = \frac{3 k sec ^{2} ( 3 x )}{2 x}

= e^{k t a n (3 x)} \frac{3 k sec ^{2} ( 3 x )}{2 x}

分式相乘:

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

= \frac{3 k e ^{k t a n (3 x)} sec ^{2} ( 3 x )}{2 x}

\int - 64 x^{3} sin (4 x^{4} + 3) d x

h \to 0 lim (\frac{( 1 + h ) ^{7} - 1}{h})

d er i v a t i v e f (x) = \frac{4}{3} x - 7

\frac{\partial}{\partial x} ((1 - x)^{2})

\frac{d}{d t} (\frac{c e ^{t}}{1 + c e ^{t}})