derivative 4^xx^4

解答

导数

4^{x} x^{4}

ln (2) \cdot 2^{2 x + 1} x^{4} + 4^{1 + x} x^{3}

求解步骤

\frac{d}{d x} (4^{x} x^{4})

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 4^{x}, g = x^{4}

= \frac{d}{d x} (4^{x}) x^{4} + \frac{d}{d x} (x^{4}) 4^{x}

\frac{d}{d x} (4^{x}) = ln (2) \cdot 2^{2 x + 1}

\frac{d}{d x} (x^{4}) = 4 x^{3}

= ln (2) \cdot 2^{2 x + 1} x^{4} + 4 x^{3} \cdot 4^{x}

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

4 \cdot 4^{x} = 4^{1 + x}

= ln (2) \cdot 2^{2 x + 1} x^{4} + 4^{1 + x} x^{3}

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

(x^{2} + y^{2}) d x + 6 x y d y = 0

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

\frac{\partial}{\partial x} (3 cos (x + y))

x \to - 100 lim (3 x^{2})