Derivative of a constant
NMT\[(C)'=0\]
NMT / ZNO
Formulas and reference
A compact mathematics reference in two levels: the NMT exam sheet and the full ZNO formula set.
ZNO — full reference
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Algebra
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19 formulas
Full ZNO
Expanded school formula set. The “NMT” badge marks formulas also present on the compact sheet.
Derivative
Derivatives
Derivative of x
NMT\[x'=1\]
Derivative of a power function
NMT\[(x^\alpha)'=\alpha x^{\alpha-1}\]
Derivative of the square root
NMT\[(\sqrt{x})'=\frac1{2\sqrt{x}}\]
Derivative of e^x
NMT\[(e^x)'=e^x\]
Derivative of a^x
\[(a^x)'=a^x\ln a\]
Derivative of ln x
NMT\[(\ln x)'=\frac1x\]
Derivative of log_a x
\[(\log_a x)'=\frac1{x\ln a}\]
Derivative of sin x
NMT\[(\sin x)'=\cos x\]
Derivative of cos x
NMT\[(\cos x)'=-\sin x\]
Derivative of tg x
NMT\[(\tg x)'=\frac1{\cos^2x}\]
Derivative of ctg x
\[(\ctg x)'=-\frac1{\sin^2x}\]
Derivative
Differentiation rules
Derivative of a sum
NMT\[(u+v)'=u'+v'\]
Derivative of a difference
NMT\[(u-v)'=u'-v'\]
Derivative of a product
NMT\[(uv)'=u'v+uv'\]
Derivative of a quotient
NMT\[\left(\frac uv\right)'=\frac{u'v-uv'}{v^2}\]
Condition
\(v\ne0\)
Constant factor rule
NMT\[(Cu)'=Cu'\]
Derivative of a composite function
\[(f(g(x)))'=f'(g(x))g'(x)\]
Derivative
Applications of derivatives
Equation of a tangent line
\[y=f(x_0)+f'(x_0)(x-x_0)\]
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