Задача 2 (Правила обчислення похідних)

Обчислити похідні заданих функцій, користуючись правилами диференціювання та таблицею похідних:

а) y=x^{3}-2x^{2}+4x-13 ;

б) y=lnx\cdot 8^{x} ;

в) y=5\sqrt[5]{x^{7}} ;

г)  y=\frac{sinx}{cosx-1}.

♦ а) y'=3x^{2}-4x+4 ;

б)  y'=(lnx)'\cdot 8^{x}+lnx\cdot (8^{x})'=\frac{1}{x}\cdot 8^{x} + lnx \cdot ln8\cdot8^{x};

в) y'=(5\sqrt[5]{x^{7}})'=(5x^{\frac{7}{5}})'=5\cdot \frac{7}{5}\cdot x^{\frac{7}{5}-1}=7x^{\frac{2}{5}}=7\sqrt[5]{x^{2}} ;

г)  y'=\frac{sin'x(cosx - 1)-sinx(cosx-1)'}{(cosx-1)^{2}}=\frac{cos^{2}x-cosx+sin^{2}x}{(cosx-1)^{2}}=

=\frac{1-cosx}{(cosx-1)^{2}}=\frac{1}{1-cosx} .♦

 

2 Responses to “Задача 2 (Правила обчислення похідних)”

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