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\({d \over dx}(c) = 0\) \({d \over dx}(x) = 1\) \({d \over dx}(cx) = c\) \({d \over dx}(x^n) = nx^{n-1}\) \({d \over dx}[sin(x)] = cos(x)\) \({d \over dx}[cos(x)] = -sin(x)\) \({d \over dx}[tan(x)] = sec^2(x)\) |
\({d \over dx}{[sin^{-1}(x)]} = {1 \over \sqrt {1-x^2}}\) \({d \over dx}{[cos^{-1}(x)]} = {-1 \over \sqrt {1-x^2}}\) \({d \over dx}{[tan^{-1}(x)]} = {1 \over 1+x^2}\) \({d \over dx}{e^x} = e^x\) \({d \over dx}{a^x} = a^x ln(a)\) \({d \over dx}{[ln(x)]} = {1 \over x}\) \({d \over dx}{[log_a(x)]} = {1 \over {x\: ln (a)}}\) |