展开 12x^{12x}(ln(x)+1)*(sin^{6x}(x))

解答

展开

12 x^{12 x} (ln (x) + 1) \cdot (sin^{6 x} (x))

12 x^{12 x} ln (x) sin^{6 x} (x) + 12 x^{12 x} sin^{6 x} (x)

求解步骤

12 x^{12 x} (ln (x) + 1) (sin^{6 x} (x))

= 12 x^{12 x} (sin^{6 x} (x)) (ln (x) + 1)

使用分配律:

a (b + c) = ab + a c

a = 12 x^{12 x} (sin^{6 x} (x)), b = ln (x), c = 1

= 12 x^{12 x} (sin^{6 x} (x)) ln (x) + 12 x^{12 x} (sin^{6 x} (x)) \cdot 1

= 12 x^{12 x} (sin^{6 x} (x)) ln (x) + 12 \cdot 1 \cdot x^{12 x} (sin^{6 x} (x))

化简

12 x^{12 x} (sin^{6 x} (x)) ln (x) + 12 \cdot 1 \cdot x^{12 x} (sin^{6 x} (x)) : 12 x^{12 x} ln (x) sin^{6 x} (x) + 12 x^{12 x} sin^{6 x} (x)

= 12 x^{12 x} ln (x) sin^{6 x} (x) + 12 x^{12 x} sin^{6 x} (x)

s im pl i f y (\frac{3 a}{5} + \frac{b}{2}) (\frac{3 a}{5} - \frac{b}{2})

e x p an d - \frac{10 ( - x + 2 )}{( x + 1 ) ^{4}}

e x p an d (4 x^{2} - \frac{3}{2 x})^{12}

e x p an d - \frac{sec ^{2} ( \frac{x}{2} )}{( tan ( \frac{x}{2} ) - 1 ) ^{2}}

e x p an d - \frac{1}{8} (36 x - 16 y)