derivative of 2^{x+y}

解答

\frac{d}{d x} (2^{x + y})

ln (2) \cdot 2^{x + y} (1 + \frac{d y}{d x})

求解步骤

\frac{d}{d x} (2^{x + y})

使用指数法则:

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

2^{x + y} = e^{(x + y) l n (2)}

= \frac{d}{d x} (e^{(x + y) l n (2)})

使用连锁律:

e^{(x + y) l n (2)} \frac{d}{d x} ((x + y) ln (2))

= e^{(x + y) l n (2)} \frac{d}{d x} ((x + y) ln (2))

\frac{d}{d x} ((x + y) ln (2)) = ln (2) (1 + \frac{d y}{d x})

= e^{(x + y) l n (2)} ln (2) (1 + \frac{d y}{d x})

e^{(x + y) l n (2)} = 2^{x + y}

= ln (2) \cdot 2^{x + y} (1 + \frac{d y}{d x})

s im pl i f y x^{2} (4 - x)^{2}

s im pl i f y - 13 \cdot 7 e^{- t}

s im pl i f y e^{- 3} \cdot e^{x}

s im pl i f y - e^{- a}