derivative of tan(e^{2x}+e^{tan(2x)})

解答

\frac{d}{d x} (tan (e^{2 x}) + e^{t a n (2 x)})

sec^{2} (e^{2 x}) e^{2 x} \cdot 2 + e^{t a n (2 x)} sec^{2} (2 x) \cdot 2

求解步骤

\frac{d}{d x} (tan (e^{2 x}) + e^{t a n (2 x)})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (tan (e^{2 x})) + \frac{d}{d x} (e^{t a n (2 x)})

\frac{d}{d x} (tan (e^{2 x})) = sec^{2} (e^{2 x}) e^{2 x} \cdot 2

\frac{d}{d x} (e^{t a n (2 x)}) = e^{t a n (2 x)} sec^{2} (2 x) \cdot 2

= sec^{2} (e^{2 x}) e^{2 x} \cdot 2 + e^{t a n (2 x)} sec^{2} (2 x) \cdot 2

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

\int_{0}^{\infty} 5^{- x} d x

\int sec^{4} (x) d x

l a pl a ce t r an s f or m f (t) = t^{4}

d er i v a t i v e (1436.53) \cdot (1.01395)^{t}