Pengertian
Turunan fungsi aljabar adalah fungsi lain dari fungsi-fungsi sebelumnya.
Rumus
\[f(x) = k \to f'(x) = 0\]
\[f(x) = x \to f'(x) = 1\]
\[f(x) = x^n \to f'(x) = nx^{n-1}\]
\[f(x) = kx^n \to f'(x) = knx^{n-1}\]
\[f(x) = k \cdot u \to f'(x) = k \cdot u'(x)\]
\[f(x) = u(x) \cdot v(x) \to f'(x) = u'(x) \cdot v(x) + u(x) \cdot v'(x)\]
\[f(x) = u(x) + v(x) \to f'(x) = u'(x) + v'(x)\]
\[f(x) = u(x) – v(x) \to f'(x) = u'(x) – v'(x)\]
\[f(x) = \frac{u(x)}{v(x)} \to f'(x) = \frac{u'(x) \cdot v(x) – u(x) \cdot v'(x)}{v^2(x)}\]
\[f(x) = u^n \to f'(x) = n \cdot u^{n-1}\cdot u'(x)\]
Contoh
\[f(x) = x^5\]
Tentukan turunan pertama dari fungsi diatas!
\[f(x) = x^n \to f'(x) = nx^{n-1}\]
\[f(x) = x^5 \to f'(x) = 5x^{5-1}\]
\[f'(x) = 5x^4\]