Question

Помогите решить, пожалуйста

Answer 1

$8)y=4x^{4} +7x^{3} -32x-18\\\\y'=4\cdot(x^{4})'+7\cdot(x^{3})'-32\cdot x' -18'=4\cdot4x^{3} +7\cdot 3x^{2}-32\cdot 1-0=\\\\=\boxed{16x^{3}+21x^{2}-32} \\\\\\9)Sin^{2}x+2Sinx=-Cos^{2}x \\\\Sin^{2}x+2Sinx+Cos^{2}x =0\\\\Sin^{2}x+2Sinx+1-Sin^{2}x =0\\\\2Sinx+1=0\\\\2Sinx=-1\\\\Sinx=-\dfrac{1}{2}\\\\x=(-1)^{n} arcSin(-\dfrac{1}{2})+\pi n,n\in Z\\\\\boxed{x=(-1)^{n+1}\frac{\pi }{6}+\pi n,n\in Z }$