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Derivative Practice
Use Basic Rules of Differentiation
Question | Answer |
---|---|
f(x)=√(3x^2+1) | f'(x)=6x/(2√(3x^2+1)) |
f(t)=√(t)-1/√(t) | f'(t)=1/(2√(t))+1/(2t^(3/2)) |
f(x)=5x^8-2x^5+6 | f'(x)=40x^7-10x^4 |
h(x)=f(g(x)) | h'(x)=f'(g(x))g'(x) |
u(x)=f(x)/g(x) | u'(x)=(g(x)f'(x)-f(x)g'(x))/(g(x))^2 |
w(x)=f(x)g(x) | w'(x)=f'(x)g(x)+f(x)g'(x) |
f(x)=x^n, n=any real number | f'(x)=nx^(n-1) |
h(x)=f(x)+g(x) | h'(x)=f'(x)+g'(x) |
f(x)=(2t)/(4+t^2) | f'(x)=(8-2t^2)/(4+t^2)^2 |