derivative of (3x-5ye^{2y-4x})

解答

\frac{d}{d x} ((3 x - 5 y) e^{2 y - 4 x})

(3 - 5 \frac{d y}{d x}) e^{2 y - 4 x} + e^{2 y - 4 x} (2 \frac{d y}{d x} - 4) (3 x - 5 y)

求解步骤

\frac{d}{d x} ((3 x - 5 y) e^{2 y - 4 x})

使用微分乘法定则:

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

f = 3 x - 5 y, g = e^{2 y - 4 x}

= \frac{d}{d x} (3 x - 5 y) e^{2 y - 4 x} + \frac{d}{d x} (e^{2 y - 4 x}) (3 x - 5 y)

\frac{d}{d x} (3 x - 5 y) = 3 - 5 \frac{d y}{d x}

\frac{d}{d x} (e^{2 y - 4 x}) = e^{2 y - 4 x} (2 \frac{d y}{d x} - 4)

= (3 - 5 \frac{d y}{d x}) e^{2 y - 4 x} + e^{2 y - 4 x} (2 \frac{d y}{d x} - 4) (3 x - 5 y)

\int - 3 sin^{2} (x) d x

d er i v a t i v e y = x^{- 5 c o s (x)}

d er i v a t i v e x ln (x) - x

\int \frac{x + 4}{x ^{2} + 6 x - 16} d x

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