derivative of 7^{x+arccos(x})

解答

\frac{d}{d x} (7^{x + a r c c o s (x)})

ln (7) \cdot 7^{x + a r c c o s (x)} (1 - \frac{1}{1 - x ^{2}})

求解步骤

\frac{d}{d x} (7^{x + a r c c o s (x)})

使用指数法则:

a^{b} = e^{b l n (a)}

7^{x + a r c c o s (x)} = e^{(x + a r c c o s (x)) l n (7)}

= \frac{d}{d x} (e^{(x + a r c c o s (x)) l n (7)})

使用连锁律:

e^{(x + a r c c o s (x)) l n (7)} \frac{d}{d x} ((x + arccos (x)) ln (7))

= e^{(x + a r c c o s (x)) l n (7)} \frac{d}{d x} ((x + arccos (x)) ln (7))

\frac{d}{d x} ((x + arccos (x)) ln (7)) = ln (7) (1 - \frac{1}{1 - x ^{2}})

= e^{(x + a r c c o s (x)) l n (7)} ln (7) (1 - \frac{1}{1 - x ^{2}})

e^{(x + a r c c o s (x)) l n (7)} = 7^{x + a r c c o s (x)}

= ln (7) \cdot 7^{x + a r c c o s (x)} (1 - \frac{1}{1 - x ^{2}})

y^{^{''}} + 4 y^{^{'}} + 20 y = 0

\frac{\partial}{\partial x} (0.0099999)

\int 1 + 5 x^{4} (20 x^{3}) d x

n = 1 \sum \infty n (\frac{3}{2})^{n}

\frac{d}{d x} ((\frac{x ^{2} + 1}{x ^{2} - 1})^{4})