derivative of (8x+15^{12}(x^3+7)^{13})

解答

\frac{d}{d x} ((8 x + 15)^{12} (x^{3} + 7)^{13})

96 (8 x + 15)^{11} (x^{3} + 7)^{13} + 39 x^{2} (x^{3} + 7)^{12} (8 x + 15)^{12}

求解步骤

\frac{d}{d x} ((8 x + 15)^{12} (x^{3} + 7)^{13})

使用微分乘法定则:

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

f = (8 x + 15)^{12}, g = (x^{3} + 7)^{13}

= \frac{d}{d x} ((8 x + 15)^{12}) (x^{3} + 7)^{13} + \frac{d}{d x} ((x^{3} + 7)^{13}) (8 x + 15)^{12}

\frac{d}{d x} ((8 x + 15)^{12}) = 96 (8 x + 15)^{11}

\frac{d}{d x} ((x^{3} + 7)^{13}) = 39 x^{2} (x^{3} + 7)^{12}

= 96 (8 x + 15)^{11} (x^{3} + 7)^{13} + 39 x^{2} (x^{3} + 7)^{12} (8 x + 15)^{12}

\int \frac{x - 9 x ^{2}}{x} d x

\frac{d y}{3 x + e ^{x}} = e^{- y} d x

e x p an d csc (x) (x + cot (x))

d er i v a t i v e x^{7} e^{x}

\frac{d y}{d x} = 2 y + a