## Important Theorems in Calculus

Calculus allows us to get analyses of a function’s behavior over the time. Calculus includes the derivatives and integrals. The basic theorem in calculus defines the relationship between derivatives and integrals. There are several theorems that define important features of the derivative and integral values of functions. Fundamental Theorem of Calculus The first part of […]

## Table of Derivatives Complex Functions

$$c’=0,\quad c=const;$$ $$(u(x)^\alpha)’=\alpha u^{\alpha-1}(x)u'(x), \quad x\in \mathbb{R}, \alpha\in \mathbb{R};$$ $$(a^{u(x)})’=a^{u(x)}\ln a\cdot u'(x),\quad a>0, a\neq 1, x\in \mathbb{R};$$ $$(e^u(x))’=e^{u(x)}u'(x);$$ $$(\log_a u(x))’=\frac{1}{u(x)\ln a}u'(x), \quad x>0;$$ $$(\log_a|u(x)|)’=\frac{1}{u(x)\ln a}u'(x),\quad x\neq 0;$$ $$(\ln u(x))’=\frac{1}{u(x)}u'(x),\quad x>0;$$ $$(\sin u(x))’=\cos u(x) \cdot u'(x), \quad x\in \mathbb{R};$$ $$(\cos u(x))’=-\sin u(x) \cdot u'(x)\quad x\in \mathbb{R};$$ $$(\mathrm{tg} u'(x))’=\frac{1}{\cos^2 u'(x)}u'(x),\quad x\neq \frac{\pi}{2}(2n+1), \in \mathbb{Z};$$ \((\mathrm{ctg} u(x))’=-\frac{1}{\sin^2 u(x)}u'(x),\quad […]

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