derivative of 2^{x^2+3x}

解答

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

ln (2) \cdot 2^{x^{2} + 3 x} (2 x + 3)

求解步骤

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

使用指数法则:

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

2^{x^{2} + 3 x} = e^{(x^{2} + 3 x) l n (2)}

= \frac{d}{d x} (e^{(x^{2} + 3 x) l n (2)})

使用连锁律:

e^{(x^{2} + 3 x) l n (2)} \frac{d}{d x} ((x^{2} + 3 x) ln (2))

= e^{(x^{2} + 3 x) l n (2)} \frac{d}{d x} ((x^{2} + 3 x) ln (2))

\frac{d}{d x} ((x^{2} + 3 x) ln (2)) = ln (2) (2 x + 3)

= e^{(x^{2} + 3 x) l n (2)} ln (2) (2 x + 3)

e^{(x^{2} + 3 x) l n (2)} = 2^{x^{2} + 3 x}

= ln (2) \cdot 2^{x^{2} + 3 x} (2 x + 3)

\int (x + 5) cos (x) d x

\int x cos^{2} (9 x) d x

\frac{d y}{d x} = 4 x e^{y}

\frac{d}{d x} ((x^{3} + 1) (3 - 2 x^{3}))

s l o p e (3, 2), (5, 6)