F'(x) = (x⁴)' - 4(x³)' + 6(x²)' - 7' = 4x³ - 12x² + 12x
f'(x) = 7(x⁵)' - 9(x³)' + 3(x)' - (3,5)' = 35x⁴- 27x² + 3
f'(x) = (x³ - 2x)' * ( x² + 3) + (x³ - 2x) * (x² + 3)' = (3x² - 2)(x² + 3) +
+ (x³ - 2x) * 2x = 3x⁴ + 9x² - 2x² - 6 + 2x⁴ - 4x² = 5x⁴ +3x² - 6
![f'(x) = \frac{( x^{2} -5)'*(2x+4)-( x^{2} -5)*(2x+4)'}{(2x+4) ^{2} } = \frac{2x*(2x+4)-2( x^{2} -5)}{(2x+4) ^{2} }= f'(x) = \frac{( x^{2} -5)'*(2x+4)-( x^{2} -5)*(2x+4)'}{(2x+4) ^{2} } = \frac{2x*(2x+4)-2( x^{2} -5)}{(2x+4) ^{2} }=](https://tex.z-dn.net/?f=f%27%28x%29+%3D++%5Cfrac%7B%28+x%5E%7B2%7D+-5%29%27%2A%282x%2B4%29-%28+x%5E%7B2%7D+-5%29%2A%282x%2B4%29%27%7D%7B%282x%2B4%29+%5E%7B2%7D+%7D+%3D+%5Cfrac%7B2x%2A%282x%2B4%29-2%28+x%5E%7B2%7D+-5%29%7D%7B%282x%2B4%29+%5E%7B2%7D+%7D%3D+++)
![= \frac{4 x^{2} +8x-2 x^{2} +10}{(2x+4) ^{2} }= \frac{2 x^{2} +8x+10}{4(x+2) ^{2} }= \frac{2( x^{2} +4x+5)}{4(x+2) ^{2} } = \frac{ x^{2} +4x+5}{2(x+2) ^{2} } = \frac{4 x^{2} +8x-2 x^{2} +10}{(2x+4) ^{2} }= \frac{2 x^{2} +8x+10}{4(x+2) ^{2} }= \frac{2( x^{2} +4x+5)}{4(x+2) ^{2} } = \frac{ x^{2} +4x+5}{2(x+2) ^{2} }](https://tex.z-dn.net/?f=%3D+%5Cfrac%7B4+x%5E%7B2%7D+%2B8x-2+x%5E%7B2%7D+%2B10%7D%7B%282x%2B4%29+%5E%7B2%7D+%7D%3D+%5Cfrac%7B2+x%5E%7B2%7D+%2B8x%2B10%7D%7B4%28x%2B2%29+%5E%7B2%7D+%7D%3D+%5Cfrac%7B2%28+x%5E%7B2%7D+%2B4x%2B5%29%7D%7B4%28x%2B2%29+%5E%7B2%7D+%7D+%3D+%5Cfrac%7B+x%5E%7B2%7D+%2B4x%2B5%7D%7B2%28x%2B2%29+%5E%7B2%7D+%7D+++)