derivative of 5^{xsin(x})

解答

\frac{d}{d x} (5^{x s i n (x)})

ln (5) \cdot 5^{x s i n (x)} (sin (x) + x cos (x))

求解步骤

\frac{d}{d x} (5^{x s i n (x)})

使用指数法则:

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

5^{x s i n (x)} = e^{x s i n (x) l n (5)}

= \frac{d}{d x} (e^{x s i n (x) l n (5)})

使用连锁律:

e^{x s i n (x) l n (5)} \frac{d}{d x} (x sin (x) ln (5))

= e^{x s i n (x) l n (5)} \frac{d}{d x} (x sin (x) ln (5))

\frac{d}{d x} (x sin (x) ln (5)) = ln (5) (sin (x) + x cos (x))

= e^{x s i n (x) l n (5)} ln (5) (sin (x) + x cos (x))

e^{x s i n (x) l n (5)} = 5^{x s i n (x)}

= ln (5) \cdot 5^{x s i n (x)} (sin (x) + x cos (x))

t an g e n t f (x) = 2 x^{3}, at x = 1

\frac{d}{d t} (\frac{1}{1 + 24 e ^{- 0.28 t}})

x y^{^{'}} + 2 y = 3 x, y (1) = 5

\int \frac{x}{( x ^{2} + 2 ) ^{\frac{4}{3}}} d x

y^{^{'}} = 3 y - y^{2}