中考函數(shù)求導(dǎo)題目及答案一、選擇題1.已知函數(shù)\(f(x)=2x^3-3x^2+1\)，求導(dǎo)數(shù)\(f'(x)\)。A.\(6x^2-6x\)B.\(6x^2-6x+1\)C.\(6x^2-6x+2\)D.\(6x^2-6x-1\)答案：A2.函數(shù)\(g(x)=x^2+4x+3\)的導(dǎo)數(shù)\(g'(x)\)是多少？A.\(2x+4\)B.\(2x+3\)C.\(2x+2\)D.\(2x-4\)答案：A3.求函數(shù)\(h(x)=\frac{1}{x}\)的導(dǎo)數(shù)\(h'(x)\)。A.\(-\frac{1}{x^2}\)B.\(\frac{1}{x^2}\)C.\(-\frac{1}{x}\)D.\(\frac{1}{x}\)答案：A二、填空題4.函數(shù)\(y=5x^4-7x^3+2x\)的導(dǎo)數(shù)是\(y'=\_\_\_\_\)。答案：\(20x^3-21x^2+2\)5.函數(shù)\(y=3x^2-5x+7\)的導(dǎo)數(shù)是\(y'=\_\_\_\_\)。答案：\(6x-5\)6.函數(shù)\(y=\sqrt{x}\)的導(dǎo)數(shù)是\(y'=\_\_\_\_\)。答案：\(\frac{1}{2\sqrt{x}}\)三、解答題7.求函數(shù)\(f(x)=x^3-6x^2+9x-4\)的導(dǎo)數(shù)，并求\(f'(2)\)的值。解：首先求導(dǎo)數(shù)\(f'(x)\)：\[f'(x)=3x^2-12x+9\]然后計(jì)算\(f'(2)\)：\[f'(2)=3(2)^2-12(2)+9=12-24+9=-3\]答案：\(f'(x)=3x^2-12x+9\)，\(f'(2)=-3\)8.已知函數(shù)\(g(x)=2x^3+5x^2-3x+7\)，求導(dǎo)數(shù)\(g'(x)\)并計(jì)算\(g'(-1)\)。解：首先求導(dǎo)數(shù)\(g'(x)\)：\[g'(x)=6x^2+10x-3\]然后計(jì)算\(g'(-1)\)：\[g'(-1)=6(-1)^2+10(-1)-3=6-10-3=-7\]答案：\(g'(x)=6x^2+10x-3\)，\(g'(-1)=-7\)9.函數(shù)\(h(x)=e^x\)的導(dǎo)數(shù)是\(h'(x)\)，求\(h'(0)\)。解：函數(shù)\(h(x)=e^x\)的導(dǎo)數(shù)是\(h'(x)=e^x\)。計(jì)算\(h'(0)\)：\[h'(0)=e^0=1\]答案：\(h'(x)=e^x\)，\(h'(0)=1\)10.函數(shù)\(k(x)=\ln(x)\)的導(dǎo)數(shù)是\(k'(x)\)，求\(k'(1)\)。解：函數(shù)\(k(x)=\ln(x)\)的導(dǎo)數(shù)是\(k'(x)=\frac{1}{x}\)。計(jì)算\(k'(1)\)：