derivative of x^5-5^x

解答

\frac{d}{d x} (x^{5} - 5^{x})

5 x^{4} - 5^{x} ln (5)

求解步骤

\frac{d}{d x} (x^{5} - 5^{x})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{5}) - \frac{d}{d x} (5^{x})

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (5^{x}) = 5^{x} ln (5)

= 5 x^{4} - 5^{x} ln (5)

t an g e n t f (x) = e^{x} cos (x)

t an g e n t \frac{x}{x + 6}

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

x \to 0 lim (\frac{5 x ^{2}}{x ^{2}})

\int_{- 1}^{1} π (1 - x^{2})^{2} d x