derivative of 4^{3sin(x-e^x})

解答

\frac{d}{d x} (4^{3 s i n (x) - e^{x}})

ln (2) \cdot 2^{2 (3 s i n (x) - e^{x}) + 1} (3 cos (x) - e^{x})

求解步骤

\frac{d}{d x} (4^{3 s i n (x) - e^{x}})

使用指数法则:

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

4^{3 s i n (x) - e^{x}} = e^{(3 s i n (x) - e^{x}) l n (4)}

= \frac{d}{d x} (e^{(3 s i n (x) - e^{x}) l n (4)})

使用连锁律:

e^{(3 s i n (x) - e^{x}) l n (4)} \frac{d}{d x} ((3 sin (x) - e^{x}) ln (4))

= e^{(3 s i n (x) - e^{x}) l n (4)} \frac{d}{d x} ((3 sin (x) - e^{x}) ln (4))

\frac{d}{d x} ((3 sin (x) - e^{x}) ln (4)) = 2 ln (2) (3 cos (x) - e^{x})

= e^{(3 s i n (x) - e^{x}) l n (4)} \cdot 2 ln (2) (3 cos (x) - e^{x})

化简

e^{(3 s i n (x) - e^{x}) l n (4)} \cdot 2 ln (2) (3 cos (x) - e^{x}) : ln (2) \cdot 2^{2 (3 s i n (x) - e^{x}) + 1} (3 cos (x) - e^{x})

= ln (2) \cdot 2^{2 (3 s i n (x) - e^{x}) + 1} (3 cos (x) - e^{x})

d er i v a t i v e (3 P + 8)^{7}

y^{^{''}} = 6.1 e^{(- 2.7 t)}

t an g e n t ln (x^{2} - 24) = x - y + 6, (- 5, 1)

\int (x^{2} - 5 x + 5) d x

\int 2 (sin (x) - cos (x) + 1) d x