derivative of e^xcos(x^2)

解答

\frac{d}{d x} (e^{x} cos (x^{2}))

e^{x} cos (x^{2}) - 2 e^{x} x sin (x^{2})

求解步骤

\frac{d}{d x} (e^{x} cos (x^{2}))

使用微分乘法定则:

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

f = e^{x}, g = cos (x^{2})

= \frac{d}{d x} (e^{x}) cos (x^{2}) + \frac{d}{d x} (cos (x^{2})) e^{x}

\frac{d}{d x} (e^{x}) = e^{x}

\frac{d}{d x} (cos (x^{2})) = - sin (x^{2}) \cdot 2 x

= e^{x} cos (x^{2}) + (- sin (x^{2}) \cdot 2 x) e^{x}

化简

= e^{x} cos (x^{2}) - 2 e^{x} x sin (x^{2})

y \to - 1 lim (- y^{5} - 3 y^{4})

t an g e n t f (x) = e^{2 x}, (0, 1)

n = 1 \sum \infty (- 1)^{n} n^{- 1}

y^{^{''}} + 5 y^{^{'}} = e^{- t}, y (0) = 0, y^{^{'}} (0) = 0

\frac{\partial}{\partial z} (e^{x} + yz)