Question

Помогите с алгеброй​

Answer 1

$f(x)=x^9+x^{15}\ \ ,\ \ f'(x)+9x^8+15x^{14}\\\\f(x)=6x^{12}-8x^7+\dfrac{1}{2}\, x^3\ \ ,\ \ \ f'(x)=72x^{11}-56x^6+\dfrac{3}{2}\, x^2\\\\f(x)=x^{-25}\ \ \ ,\ \ \ f'(x)=-25\cdot x^{-26}=-\dfrac{25}{x^{26}}\\\\\\f(x)=4sinx-\dfrac{1}{cos^2x}\ \ ,\ \ f'(x)=4\, cosx-\dfrac{-2\, cosx\cdot (-sinx)}{cos^4x}=4\, cosx-\dfrac{2\, sinx}{cos^3x}\\\\{}\qquad \qquad \qquad \qquad \qquad \quad ili\ \ f'(x)=4\, sinx-\dfrac{sin2x}{cos^4x}$

$f(x)=\dfrac{1}{8}\, cosx+\dfrac{1}{2\sqrt{x}}\ \ ,\ \ f'(x)=-\dfrac{1}{8}\, sinx+\dfrac{1}{2}\cdot (-\dfrac{1}{2}\Big)\, x^{-\frac{3}{2}}=-\dfrac{1}{8}\, sinx-\dfrac{1}{4\sqrt{x^3}}$