導(dǎo)數(shù)基本入門題目及答案1.求函數(shù)\(f(x)=x^2\)在\(x=1\)處的導(dǎo)數(shù)。答案：函數(shù)\(f(x)=x^2\)的導(dǎo)數(shù)為\(f'(x)=2x\)。將\(x=1\)代入，得到\(f'(1)=2\cdot1=2\)。2.求函數(shù)\(g(x)=3x^4-2x^3+5x^2-7\)的導(dǎo)數(shù)。答案：函數(shù)\(g(x)=3x^4-2x^3+5x^2-7\)的導(dǎo)數(shù)為\(g'(x)=12x^3-6x^2+10x\)。3.求函數(shù)\(h(x)=\frac{1}{x}\)的導(dǎo)數(shù)。答案：函數(shù)\(h(x)=\frac{1}{x}\)的導(dǎo)數(shù)為\(h'(x)=-\frac{1}{x^2}\)。4.求函數(shù)\(k(x)=\sqrt{x}\)的導(dǎo)數(shù)。答案：函數(shù)\(k(x)=\sqrt{x}\)的導(dǎo)數(shù)為\(k'(x)=\frac{1}{2\sqrt{x}}\)。5.求函數(shù)\(m(x)=\ln(x)\)的導(dǎo)數(shù)。答案：函數(shù)\(m(x)=\ln(x)\)的導(dǎo)數(shù)為\(m'(x)=\frac{1}{x}\)。6.求函數(shù)\(n(x)=e^x\)的導(dǎo)數(shù)。答案：函數(shù)\(n(x)=e^x\)的導(dǎo)數(shù)為\(n'(x)=e^x\)。7.求函數(shù)\(p(x)=\sin(x)\)的導(dǎo)數(shù)。答案：函數(shù)\(p(x)=\sin(x)\)的導(dǎo)數(shù)為\(p'(x)=\cos(x)\)。8.求函數(shù)\(q(x)=\cos(x)\)的導(dǎo)數(shù)。答案：函數(shù)\(q(x)=\cos(x)\)的導(dǎo)數(shù)為\(q'(x)=-\sin(x)\)。9.求函數(shù)\(r(x)=\tan(x)\)的導(dǎo)數(shù)。答案：函數(shù)\(r(x)=\tan(x)\)的導(dǎo)數(shù)為\(r'(x)=\sec^2(x)\)。10.求函數(shù)\(s(x)=\cot(x)\)的導(dǎo)數(shù)。答案：函數(shù)\(s(x)=\cot(x)\)的導(dǎo)數(shù)為\(s'(x)=-\csc^2(x)\)。11.求函數(shù)\(t(x)=\sec(x)\)的導(dǎo)數(shù)。答案：函數(shù)\(t(x)=\sec(x)\)的導(dǎo)數(shù)為\(t'(x)=\sec(x)\tan(x)\)。12.求函數(shù)\(u(x)=\csc(x)\)的導(dǎo)數(shù)。答案：函數(shù)\(u(x)=\csc(x)\)的導(dǎo)數(shù)為\(u'(x)=-\csc(x)\cot(x)\)。13.求函數(shù)\(v(x)=x^3+2x^2-5x+7\)在\(x=2\)處的導(dǎo)數(shù)。答案：函數(shù)\(v(x)=x^3+2x^2-5x+7\)的導(dǎo)數(shù)為\(v'(x)=3x^2+4x-5\)。將\(x=2\)代入，得到\(v'(2)=3\cdot2^2+4\cdot2-5=12+8-5=15\)。14.求函數(shù)\(w(x)=\frac{1}{x^2+1}\)的導(dǎo)數(shù)。答案：函數(shù)\(w(x)=\frac{1}{x^2+1}\)的導(dǎo)數(shù)為\(w'(x)=-\frac{2x}{(x^2+1)^2}\)。15.求函數(shù)\(x(x)=x^2\ln(x)\)的導(dǎo)數(shù)。答案：函數(shù)\(x(x)=x^2\ln(x)\)的導(dǎo)數(shù)為\(x'(x)=2x\ln(x)+x^2\cdot\frac{1}{x}=2x\ln(x)+x\)。16.求函數(shù)\(y(x)=e^{2x}\)的導(dǎo)數(shù)。答案：函數(shù)\(y(x)=e^{2x}\)的導(dǎo)數(shù)為\(y'(x)=2e^{2x}\)。17.求函數(shù)\(z(x)=\ln(x^2)\)的導(dǎo)數(shù)。答案：函數(shù)\(z(x)=\ln(x^2)\)的導(dǎo)數(shù)為\(z'(x)=\frac{2x}{x^2}=\frac{2}{x}\)。18.求函數(shù)\(a(x)=\sin(2x)\)的導(dǎo)數(shù)。答案：函數(shù)\(a(x)=\sin(2x)\)的導(dǎo)數(shù)為\(a'(x)=2\cos(2x)\)。19.求函數(shù)\(b(x)=\cos(3x)\)的導(dǎo)數(shù)。答案：函數(shù)\(b(x)=\cos(3x)\)的導(dǎo)數(shù)為\(b'(x)=-3\sin(3x)\)。20.求函數(shù)\(c(x)=\tan(x^2)\)的導(dǎo)數(shù)。答案：函數(shù)\(c(x