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a) ![f(x)=(3x+2)^{0.5}+x^{4} f(x)=(3x+2)^{0.5}+x^{4}](https://tex.z-dn.net/?f=f%28x%29%3D%283x%2B2%29%5E%7B0.5%7D%2Bx%5E%7B4%7D)
![f'(x)=((3x+2)^{0.5}+x^{4})'=0.5*(3x+2)^{-0.5}*3+4x^{3}= frac{3}{2 sqrt{3x+2}}+4x^{3} f'(x)=((3x+2)^{0.5}+x^{4})'=0.5*(3x+2)^{-0.5}*3+4x^{3}= frac{3}{2 sqrt{3x+2}}+4x^{3}](https://tex.z-dn.net/?f=f%27%28x%29%3D%28%283x%2B2%29%5E%7B0.5%7D%2Bx%5E%7B4%7D%29%27%3D0.5%2A%283x%2B2%29%5E%7B-0.5%7D%2A3%2B4x%5E%7B3%7D%3D+frac%7B3%7D%7B2+sqrt%7B3x%2B2%7D%7D%2B4x%5E%7B3%7D)
b)![f(x)=(-x^{2}+2x)^{3}+(x-3)^{4} f(x)=(-x^{2}+2x)^{3}+(x-3)^{4}](https://tex.z-dn.net/?f=f%28x%29%3D%28-x%5E%7B2%7D%2B2x%29%5E%7B3%7D%2B%28x-3%29%5E%7B4%7D)
![f'(x)=((-x^{2}+2x)^{3}+(x-3)^{4})'=3*(-x^{2}+2x)^{2}*(-2x+2)+4*(x-3)^{3}=-6(x-1)(-x^{2}+2x)^{2}+4(x-3)^{3} f'(x)=((-x^{2}+2x)^{3}+(x-3)^{4})'=3*(-x^{2}+2x)^{2}*(-2x+2)+4*(x-3)^{3}=-6(x-1)(-x^{2}+2x)^{2}+4(x-3)^{3}](https://tex.z-dn.net/?f=f%27%28x%29%3D%28%28-x%5E%7B2%7D%2B2x%29%5E%7B3%7D%2B%28x-3%29%5E%7B4%7D%29%27%3D3%2A%28-x%5E%7B2%7D%2B2x%29%5E%7B2%7D%2A%28-2x%2B2%29%2B4%2A%28x-3%29%5E%7B3%7D%3D-6%28x-1%29%28-x%5E%7B2%7D%2B2x%29%5E%7B2%7D%2B4%28x-3%29%5E%7B3%7D)
c)![f(x)= sqrt{7+14x}-5x^{6} f(x)= sqrt{7+14x}-5x^{6}](https://tex.z-dn.net/?f=f%28x%29%3D+sqrt%7B7%2B14x%7D-5x%5E%7B6%7D)
![f'(x)=(sqrt{7+14x}-5x^{6})'=0.5*(7+14x)^{-0.5}*14-30x^{5}=frac{7}{sqrt{7+14x}} -30x^{5} f'(x)=(sqrt{7+14x}-5x^{6})'=0.5*(7+14x)^{-0.5}*14-30x^{5}=frac{7}{sqrt{7+14x}} -30x^{5}](https://tex.z-dn.net/?f=f%27%28x%29%3D%28sqrt%7B7%2B14x%7D-5x%5E%7B6%7D%29%27%3D0.5%2A%287%2B14x%29%5E%7B-0.5%7D%2A14-30x%5E%7B5%7D%3Dfrac%7B7%7D%7Bsqrt%7B7%2B14x%7D%7D+-30x%5E%7B5%7D)
d)![f(x)=(-4x^{3}+1)^{4}-(2-x)^{5} f(x)=(-4x^{3}+1)^{4}-(2-x)^{5}](https://tex.z-dn.net/?f=f%28x%29%3D%28-4x%5E%7B3%7D%2B1%29%5E%7B4%7D-%282-x%29%5E%7B5%7D)
![f'(x)=((-4x^{3}+1)^{4}-(2-x)^{5})'=4*(-4x^{3}+1)^{3}*12x^{2}+5(2-x)^{4}=48x^{2}*(-4x^{3}+1)^{3}+5(2-x)^{4} f'(x)=((-4x^{3}+1)^{4}-(2-x)^{5})'=4*(-4x^{3}+1)^{3}*12x^{2}+5(2-x)^{4}=48x^{2}*(-4x^{3}+1)^{3}+5(2-x)^{4}](https://tex.z-dn.net/?f=f%27%28x%29%3D%28%28-4x%5E%7B3%7D%2B1%29%5E%7B4%7D-%282-x%29%5E%7B5%7D%29%27%3D4%2A%28-4x%5E%7B3%7D%2B1%29%5E%7B3%7D%2A12x%5E%7B2%7D%2B5%282-x%29%5E%7B4%7D%3D48x%5E%7B2%7D%2A%28-4x%5E%7B3%7D%2B1%29%5E%7B3%7D%2B5%282-x%29%5E%7B4%7D)
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