1.
\(y'=\left(2x^4\right)'+\left(4x^2\right)'+\left(1\right)'=8x^3+8x\)
2.
\(y'=\left(\dfrac{1}{3}x^3\right)'-\left(\dfrac{1}{2}x^2\right)'-\left(x\right)'+\left(3\right)'=x^2-x-1\)
3.
\(y'=\left(2x^3+1\right)'\left(4x-2\right)+\left(2x^3+1\right)\left(4x-2\right)'\)
\(=6x^2\left(4x-2\right)+4\left(2x^3+1\right)\)
\(=24x^3-12x^2+8x^3+4\)
\(=32x^3-12x^2+4\)
4.
\(y'=\dfrac{\left(x^4-x^3\right)'.\left(2x^2+1\right)-\left(2x^2+1\right)'\left(x^4-x^3\right)}{\left(2x^2+1\right)^2}\)
\(=\dfrac{\left(4x^3-3x^2\right)\left(2x^2+1\right)-4x\left(x^4-x^3\right)}{\left(2x^2+1\right)}\)
\(=\dfrac{8x^5+4x^3-6x^4-3x^2-4x^5+4x^2}{\left(2x^2+1\right)^2}\)
\(=\dfrac{4x^5-6x^4+4x^3+4x^2}{\left(2x^2+1\right)^2}\)
5.
\(y'=2cos\left(4x-\dfrac{\pi}{5}\right).\left(cos\left(4x-\dfrac{\pi}{5}\right)\right)'\)
\(=2cos\left(4x-\dfrac{\pi}{5}\right).\left(-sin\left(4x-\dfrac{\pi}{5}\right)\right).\left(4x-\dfrac{\pi}{5}\right)'\)
\(=-8.cos\left(4x-\dfrac{\pi}{5}\right).sin\left(4x-\dfrac{\pi}{5}\right)\)
\(=-4sin\left(8x-\dfrac{2\pi}{5}\right)\)
6.
\(y'=\left(3\left(5x+4\right)^4\right)'\)
\(=12.\left(5x+4\right)^3.\left(5x+4\right)'\)
\(=60\left(5x+4\right)^3\)
